research article forecasting dry bulk freight index with...

Research ArticleForecasting Dry Bulk Freight Index with Improved SVM

Qianqian Han1 Bo Yan2 Guobao Ning3 and B Yu4

1 School of Accountancy Shandong University of Finance and Economics Jinan Shandong 250014 China2 Transportation Management College Dalian Maritime University Dalian 116026 China3 School of Automotive Studies Tongji University Shanghai 201804 China4 School of Traffic and Transportation Beijing Jiaotong University Beijing 100044 China

Correspondence should be addressed to Guobao Ning guobao tj163com and B Yu yubjjt126com

Received 4 March 2014 Revised 5 May 2014 Accepted 6 May 2014 Published 11 June 2014

Academic Editor Rui Mu

Copyright copy 2014 Qianqian Han et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

An improved SVMmodel is presented to forecast dry bulk freight index (BDI) in this paper which is a powerful tool for operatorsand investors to manage the market trend and avoid price risking shipping industry The BDI is influenced by many factorsespecially the random incidents in dry bulk market inducing the difficulty in forecasting of BDITherefore to eliminate the impactof random incidents in dry bulk market wavelet transform is adopted to denoise the BDI data series Hence the combined modelof wavelet transform and support vector machine is developed to forecast BDI in this paper Lastly the BDI data in 2005 to 2012are presented to test the proposed model The 84 prior consecutive monthly BDI data are the inputs of the model and the last 12monthly BDI data are the outputs of model The parameters of the model are optimized by genetic algorithm and the final modelis conformed through SVM training This paper compares the forecasting result of proposed method and three other forecastingmethodsThe result shows that the proposed method has higher accuracy and could be used to forecast the short-term trend of theBDI

1 Introduction

The BDI published by the Baltic Exchange is used asan important evaluation factor for the dry bulk marketin shipping industry It is usually consulted by shippingoperators and investors to forecast the trend of dry bulkmarket However as the price of dry bulk market changesalmost every day and the affecting factors of the price arecomplicated the prediction of the trend of dry bulk marketbecomes of difficulty Since 2001 the BDI has experienced ahuge fluctuation The value of BDI was less than 1000 pointsat that time and increased to more than 11000 points in May2008 Five months later it decreased to less than 800 pointsTherefore research on the law of shipping market freightfluctuation and the forecasting of the trend of BDI is of specialsignificance for operators and investors tomanage themarkettrend and avoid price risk in shipping industry

Since the Baltic Freight Index (BFI) was established in1985 many researchers and shipping scholars have made

in-depth research on the volatility and trend prediction ofBFI and subsequent BDI However none of the forecastingmethods is widely used in BDI prediction The remarkablework in this field has been done by Kavussanos who workedon the dry bulk market prices issues as early as the 1990sKavussanos and Visvikis [1] used VECM-GARCH modelto investigate the lead-lag relationship in both return andvolatilities between spot and future markets Cullinake [2] isalso a pioneer in developing BFI index forecasting methodwith ARIMA model After that some prediction techniquessuch as statistical regression and neural network are widelyused in BDI prediction However the method of statisticalregression is appropriate for stability normality and inde-pendence time series and not appropriate for complex timeseries Neural network has a good nonlinear approximationcapability but the model structure is difficult to determineIt is prone to excessive training or insufficient training forthe neural network which induces some shortages such astrapping in local minimum being sensitive to initial value

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 460684 12 pageshttpdxdoiorg1011552014460684

2 Mathematical Problems in Engineering

and overreliance on design skills Li and Parsons [3] used theneural network to forecast the tanker freight rate and thencompared with ARMA model They proved that the neuralnetwork model has higher prediction accuracy for a longtime series Cullinane et al [4] forecasted the spot freightrate index with a simple single variable in ARMA modelA new model-fractional integrated autocorrelation movingaverage model (ARFIMA) is presented by Granger [5] indata forecasting Based on the ARFIMA approach Henry [6]showed that almost a half of the new-coming seventeen stockmarkets in the world in the 1990s have long memory whichis similar to their searches by Crato [7] Jonahan [8] and soon

In recent years econometric models are popular infreight rate index forecasting for instance ARIMA modelVAR model and VECM model Empirical analysis showsthat the econometric models have higher accuracy than thetraditional prediction methods for nonstationary time seriesVeenstra andFranses [9] developedVARmodel in forecastingBDI based on cointegrated process of the high time series andthemethod of unit root test Kavussanos andAlizadeh-M [10]presented a single variable seasonalARIMA-SARIMAmodelmultivariable seasonal cointegrating and VAR to analyze theseasonal characteristics of dry bulk shipping market

Tvedt [11] used the unit root tests to reject the randomwalk hypothesis of freight rate confirming a state of sta-tionary in freight rates forecasting for the classical shippingmarket models Two years later a rejection of applicabilityof the expectations theory in freight market was presentedby Adland and Cullinane [12] They also proved that the riskpremium is time varying depending on the freight marketconditions and time charter duration A fuzzy-DELPHIadjustment process for improvement of accuracy was pro-posed by Duru et al [13] They also illustrate its performancein the validation of adjustments of statistical forecasts in theBDI through an empirical study Zhang et al [14] employedRS and GPH tests to model long memory of volatility of theindices based on the investigation of fluctuation features ofdry bulk shipping market with the BDI

A new machine learning method namely support vectormachine (SVM) is widely employed in many fields forinstance handwriting recognition three-dimension objectsrecognition faces recognition text images recognition voicerecognition and regression analysis [15ndash23] The SVM basedon statistical learning theory has good fitting ability forcomplex nonlinear function At the same time it can avoidtrapping problem of overfitting learning A support vectormachine-based (SVM) model is developed to predict thebaseline travel and dwell times of buses based on recent databy Yu et al [24 25] The authors [24 25] also presented ahybrid model based on support vector machine (SVM) andKalman filtering technique to predict bus arrival times Yuet al [26] also adopted support vector machine (SVM) arti-ficial neural network (ANN) 119896 nearest neighborrsquos algorithm(119896-NN) and linear regression (LR) for the bus arrival timeprediction van Gestel et al [27] research the financial timeseries prediction problems based on the least squares SVMmodel Cao and Tay [28] research the parameters of SVMselection and test their approach with empirical analysis of

financial time series The SVM model is widely used in thestock market Kim [29] compared the forecasting result ofstock price index between SVM model with the BP neuralnetwork model and the CBRmodel He proved that the SVMmodel has better prediction of financial time series Huanget al [21] applied SVM to forecast the movement direction ofNIKKEI 225 index

It is suitable for nonlinear time series prediction by theSVM since the full consideration with the randomness ofthe data sequence From the application of SVM especiallyin financial index prediction as well as freight data it is nohard to be employed in another index prediction in terms ofapplicability However SVM is rarely studied and used in thefield of BDI forecast Therefore this paper will analyze theapplicability of SVM model in BDI forecasting and make anempirical test

BDI data sequences can be regarded as signals changedover time The signals usually have characteristics such asperiodic and seasonal of dry bulk shipping market freightindex fluctuationThenoise of the signal reflects the influencefactors of freight index or random events To grasp the ruleof BDI data variation the random disturbance factors shouldbe eliminated Therefore denoising processing of the signalis necessary for an accuracy data forecasting Some methodssuch as a self-adaptive filtration method the Kalman filtermethod and average moving method are often used todenoise signal of data Yu et al [30] adapt an adaptivefiltration method in bus arrival time prediction modelHowever the method of wavelet transform is proposed todenoise the raw signal in this paper

Wavelet transform is the most widely used multiscaleanalysis method till now The root of wavelet transform isscaling and translation in the signal analysis It is a milestonein the history of the development of Fourier analysis In1982 a French oil exploration technician called J Morfettried to deal with irregular signals with wavelet methodmore effectively Research of wavelet analysis was becomingpopular after that It is widely used in image processingvoice processing and signal processing In recent years thewavelet transform method has been employed in areas offinance and economy and the empirical result showed agood effect Esteban et al [31] predicted time series withwaveletmethod Firstly they decomposed the time series intotwo different cycles in sequence with wavelet Then ARMAmodel is present in regression of each data cycle Lastly thetwo forecasting values are added to get the final predictionresults They proved that their proposed approach had betterpredicted result than ARMAmodel

Moreover some researchers also tried to establish thecombined model with the wavelet transform and SVM[32ndash39] Wu [40] proposed novel robust wavelet supportvector machine which is based on wavelet theory and themodified support vector machineThey also designed swarmoptimization algorithm to select the optimal parameters oftheir proposedmodel Two years laterWu and Law [41]madean in-depth research based on the wavelet support vectormachine proposed byWu [40]Wavelet transform is also usedby Guo to map the sample data into several time-frequencydomains He then developed the SVM model to forecast the

Mathematical Problems in Engineering 3

gross value of textile products in Japan precisely A wavelettransform and SVM combined model is developed by Hsiehand Chen to predict the dissolved oxygen density in water-quality processTheir results showed a higher accuracy of thecombinedmodel than BP neural networkmodel Liu and Fan[42] stated that the performance of SVM can be improvedwith the introducing of discrete wavelet transform Wanget al [43] used the wavelet transform to decompose the damdeformation time series into different frequency componentsand then forecast the series with a SVM model A waveletkernel function for SVM is presented by Wei and Lin [17]they also denoised the signal with multiscale interpolationand sparse attributes The performance proved that theirproposed model was accurate and convergent

Although there are many studies of the combination ofwavelet transform and SVM few have been made in drybulk freight index Therefore this paper constructs a wavelettransform and SVM combined forecast model It removesthe random factors in BDI series with wavelet and thenestablishes a SVM model The numerical analysis shows thatour method has better predicting results than the commonlyused predictionmethodsOf course as a predictionmethod itshould be tested with large numbers of tests while evaluatingthe accuracy of its prediction which is however the shortageof this paper for the time limited

This paper is organized as follows Section 2 reviewsthe data on the shipping freight market and analyzes thefuture of the BDI data Section 3 presents the decompositionand reconstruction of wavelet The forecasting models andprocedures are proposed in Section 4 A case study is shownin Section 5 and the performance of several prediction resultsis compared Besides the conclusion of this paper and therecommendations for future studies are provided in this part

2 Characters and Influence Factors of BDI

The volatility of freight is directly reflected by the fluctuationof freight indexes for example BDI In terms of marketstructure freight price depends on the supply (ship owner)and the demand (cargo) Concerning market economiesfreight price of general cargo is mainly influenced by threeexternal factors an act of war or natural disaster the globaleconomy and the market speculation

In retrospect force majeure for example war factorsis the major power driving the fluctuation of the worldshipping market especially in the turbulent times In 1956the outbreak of Suez Crisis drastically increased the shippingmarket risks throughout the world Shipping lines and areachanged a lot and supply in dry bulk shippingmarket rapidlywent down which led to the high volatility of freight priceIn 1973 the third Middle East war broke out Arab countriesfirstly used the ldquooil weaponrdquo resulting in the sharp increasingof fuel price and freight price consequently The First WorldWar the SecondWorldWar theMiddle East wars hurricanetsunamis and other natural disasters brought high risks tomaritime transport market Firstly wars and natural disasterssuch as forcemajeure occurrence or even expectation of thoseevents can affect the confidence of both ship owners and

shippers secondly once sailing area is limited such as theclose of Suez Canal during the second Middle East war theaverage travel distance will increase and the supply capacitywill drop significantly besides the rise of oil prices due towars will also increase shipping costs

Shipping derivation has shown that the world economicsituation and the development of international trade play adecisive role in the shipping market existence and changesTherefore the economic cycle and trade demand are thedurable and fundamental influences in the shipping marketThemost remarkable presentation of the impact of economicenvironment on maritime shipping was the terrible hit of theglobal economic crisis to the shipping industry Economiccrisis led to slower global economic growth and commodityprices falling sharply In the first half of 2009 the fixedcapital formation and manufacturing output of the worldrsquosmajor economies have double-digit decline Steel mills andother enterprises in order to cope with shrinking demandtake measures of limiting production or semiproductionwhich led to the demand on iron ore and coal droppingsignificantly Dry Freight Index experienced unprecedentedvolatility in the six months from the highest point in historyfalling to the lowest pointThe demand of iron ore which wasthe largest dry bulk seaborne trade at that time decreasedsignificantly China as the largest importer unloaded 30million tons of iron ore imports in Nov 2008 down by207 which was the first negative growth The impact ofeconomic crisis on supply capacity is mainly reflected inthe shipbuilding market Global economic downturn led tosharp decline in shipbuilding demand and some ship ownersbegan to cancel the order because of the shortage of moneyBecause there are one to two years of construction time fromordering to delivery the impact of the economic crisis on theshipbuilding industry has one to two years of lag extendingto freight market Therefore new ships to be delivered twoyears after ordering will substantially decrease resulting inshrinking supply capacity

Freight derivatives were created in order to avoid the riskof emergencies in shippingmarketMajor functions of freightderivatives reside in hedging and price discovery Freightderivatives include the Baltic Freight Index futures (BIFFEX)forward freight agreements (FFA) and the shipping options(freight option) Volatile freight rates since 2004 have givenspeculators profit opportunities Investment banks as Gold-man Sachs Morgan Stanley and other financial institutionsand hedge funds have entered into speculative market someshipping companies also use their information superiority toengage in the market

According to dry bulk freight index trend freight indexit disorderly changes in random variation so it is difficultto grasp the change regulation In order to better graspthe inherent regulation of fluctuations it can be dividedinto two categories the first category is the one in whichthere is a pattern existing for example the world economywith cyclical characteristics coal iron ore grain productioncapacity and shipping capacitywith seasonal fluctuations thesecond category is sudden and random factors for examplenatural climate political events average travel distance scien-tific and technological development countryrsquos international


trade policy sudden changes in trade structure economicinterest transferred exchange rate fluctuations ship archiveoperational productivity international shipping norms andmarket rumors

After the above analysis both the two factors have effecton the dry bulk freight index To grasp more accurate freightindex fluctuation characteristics what needs to be done isto dig out the historical dry bulk freight index data andthen use data processing methods to eliminate the disordercharacteristics caused by the second category of factorsBased on that the most suitable methods are used for BDIprediction

If the time series of BDI can be regarded as a kindof changeable signal with time elapsing then there is richinformation in the signal The first category includes theinformation of cyclical fluctuations of BDI As the cycle islong-term the first category factors have lower frequenciesand are located in low frequency range The second categoryfactors are stochastic irregular and unexpected Thoughthose factors occur not very often the frequency can be stillrelatively high if aggregating the second category factors intomonolithic So the high frequency range includes the secondcategory factors The discussion on cyclical fluctuation ofBDI is based on thought as follows (1) signal reconstructionExtracting BDI signal process attempts to remove stochasticirregrular and unexpected factors and noise from the BDIsignal by separating the low and the high frequency part (2)BDI is an output of a complex function as there are so manyfactors impacting on the dry bulk freight market In order toanalyze the BDI signal accurately this paper applies the SVMonto the prediction of the reconstructed signal based on theresults of extracting BDI signal process

3 Adopting the Wavelet Transform toDenoise the BDI

Useful signal is commonly presented as stationary signals orlow frequency signals while noise signal is usually unstableand has high frequency Therefore the characteristics ofBDI ensure the application of wavelet analysis to eliminatenoise signal When using wavelet analysis to remove noisesignal from shipping indexes such noise signal is mainlyincluded in high frequency wavelet coefficients for whichthe threshold method can be used for decomposing waveletcoefficients Each layer of decomposed wavelet coefficientsshould be reconstructed to eliminate the noise The purposeof removing noise signals from BDI signal 119878(119905) is to obtainactual signal 119891(119905) from 119878(119905) by which the authenticity of datacan be ensured

The one-dimension model of BDI signal with noises canbe presented as follows

119878 (119905) = 119891 (119905) + 120590119890 (119905) 119905 = 0 1 119899 minus 1 (1)

where 119891(119905) is the real signal 119890(119905) is the noise 120590 is the noiseintensity 119878(119905) is the signal with noises

The process of wavelet noise reduction is the processof decomposition and reconstruction for signal Originalfunction or signal is split into several relevant pieces without

Original data

High-pass filterdecomposition

Low-pass filterdecomposition

High-passseries

Low-passsequence

High-passfilter synthesis

Low-passfilter synthesis

Denoising data

Figure 1 Decomposition and reconstruction of wavelet transformdenoising process

losing much information Those pieces are such waveletwhich changes in scale and decays in timeThewavelet recon-struction is the process where those pieces are combined torestore the real features

The decomposition and reconstruction of wavelet areshown as in Figure 1

BDI is one-dimension time series and the wavelet denois-ing process against such kind of signal is usually expressed asthe procedure presented as follows

Step 1 Preprocessing the data which include noises for usingin next steps

Step 2 Wavelet denoising process to the one-dimensionsignal Selecting a suitable wavelet mother function andsetting an appropriate decomposing layer 119873 Decomposing119878(119905) into119873 layers

Step 3 Quantizing the threshold of wavelet decompositioncoefficients Selecting a suitable threshold for the high fre-quency coefficient of each layer

Step 4 Inverse transform of one-dimension wavelet Basedon the coefficient of 119873th layer and the quantized highfrequency coefficients from 1st to 119873th layer reconstructingthe one-dimension signal The reconstructed signal is thedenoised signal


Theoretical base of wavelet denoising is presented asfollows

120595(119905) is a function where Fourier transform exists Ifits Fourier transform (119905) meets the condition int

infin

minusinfin

((119905)2

119908)119889119908 lt infin the function can be a wavelet function Suppos-ing 119895 isin 119885 and 120595

2119895(119905) is the dyadic stretching transformation

of 120595(119905) against factor 2119895 then 1205952119895(119905) can be expressed as

1205952119895 (119905) =

1

2119895120595(

119905

2119895) (2)

Wavelet transform of function 119891(119905) with scale 2119895 at

position 119905 can be defined as the convolution of119891(119905) and1205952119895(119905)

presented as

1198822119895119891 (119905) = 119891 times 120595

2119895 (119905) (3)

For wavelet function120595(119905) supposing there exist constants119860 and 119861 and 0 lt 119860 le 119861 lt infin then we can get

forall120596 isin 119877 119860 le

infin

sum

119895=minusinfin

(2119895

120596) le 119861 (2) (4)

where (119905) is the Fourier transform of 120595(119905) Then 120595(119905) can becalled dyadic wavelet function and the correspondingwavelettransform can be called dyadic wavelet transform

For any function 120594(119905) with Fourier transform if itsFourier transform meets Subject (5)

infin

sum

119895=minusinfin

(2119895

120596)120594 (2119895

120596) = 1 (5)

then it can be called reconstruction wavelet It can be easilyfound that there are countless functions 120594(119905)meeting Subject(5)

The dyadic wavelet transform is complete and stableThe ldquocompleterdquo means that the function can be restored byits dyadic wavelet transform In terms of energy ldquostablerdquomeans that the total ability of dyadic wavelet transformhas limitation which is close to the energy of the functionFunction 119891(119905) isin 119871

2

(119877) can be restored by its dyadic wavelettransform and the corresponding reconstruction wavelet onthe basis of

119891 (119905) =

infin

sum

minusinfin

1198822119895119891 times 120594

2119895 (119905) (6)

119860100381710038171003817100381711989110038171003817100381710038172

le

infin

sum

119895=minusinfin

10038171003817100381710038171198822119895119891 (119905)10038171003817100381710038172

le 119861100381710038171003817100381711989110038171003817100381710038172

(7)

In practical application the measurable resolution ofsignal is limited so it is impossible to conduct wavelettransform on all scales 2119895 (minusinfin lt 119894 lt infin) Therefore 2119895should be set as a limited value The wavelet transform isconfined between a limited maximum scale 119895 = 119869 and alimited minimum scale 119895 = 1 2119868 is the highest resolutionand 2119869 is the lowest resolutionWith respect to resolution it isrelevant to frequency That is to say the higher the frequency

is the higher the resolution is and vice versa To expressthe signal resolution decomposition of wavelet transforma real function 120593(119905) is introduced hereafter whose Fouriertransform should meet Subject (8) Consider

120593(119905)2

=

+infin

sum

119895=1

(2119895

120596)120594 (2119895

120596) (8)

According to (3) and (6) it can be easily obtained that

120593(0)2

= lim119896rarr0

(2119896

120596)2

= lim119896rarr0

(2119895

120596)120594 (2119895

120596) = 1

120593(infin)2

= lim119896rarr+infin

(2119896

120596)2


(2119895

120596)120594 (2119895

120596) = 1

(9)

Equation (9) indicates that the energy of 120593(120596) gathers inthe low frequency range so 120593(119905) is a smooth function withlow-pass characteristics A smooth operator 119878

2119895 is defined as

follows1198782119895119891 (119905) = 119891 lowast 120593

2(119905)

1205932(119905) =

1

2119895120593(

119905

2119895)

(10)

where 1198782119895119891(119905) denotes the low-pass filtering component of

signal 119891(119905) when the resolution is 2119895 The high frequencycomponent of 119891(119905) is not presented in 119878

2119895119891(119905) but in the

dyadic wavelet transform 1198822119895119891(119905)

1le119895le119869between scales 2119868

and 2119869 so 119882

2119895119891(119905) stands for the detailed component and

1198782119895119891(119905)means the low-pass smooth component of the signal

The signal details (the high frequency ingredient) containedin 1198782119895119891(119905) decrease with 2119895 increasing and the lost informa-

tion can still be restored by the wavelet transform1198822119895119891(119905)

The time series is defined as 1198781198890

2119891 and the low-pass

smooth component at scale 2119895 is defined as 1198781198891198952119891 According to

(7) 1198781198891198952119891 can be split into the low and the high half frequency

denoted by 119878119889119895

2+ 1119891 and 119882

119889119895

2+ 1119891 respectively The 119889 is

the concrete signal The decomposition algorithm of 1198781198891198952119891 is

shown as follows

119895 = 0while (119895 lt 119869)

119882119889119895

2+ 1119891 = (1120582

119895)119878119889119895

2119891 lowast 119866

119895

119878119889119895

2+ 1119891 = 119878

119889119895

2lowast 119867119895

119895 = 119895 + 1the end

The reconstruction algorithm of 11987811988902119891 is shown as follows

119895 = 119869while (119895 gt 0)

119878119889119895

2+ 1119891 = 120582

119895119882119889119895

2119891 lowast 119870

119895minus1+ 119878119889119895

2119891 lowast 119867

119895minus1

119895 = 119895 minus 1the end

where 119866119895119867119895 and119870

119895are a group of corresponding filters


Observer

Observer

Slack variable

Slack variable

Predicted values

Y

X

120576

120576ℏ

ℏ

Figure 2 The 120576-insensitivity tube of SVM

4 Forecasting BDI with SVM

41 Support Vector Machine The support vector machineis a kind of machine learning system with the purpose ofmaximizing the margin distance between different categoriesof problems [44ndash46] The model of SVM is as follows

119891 (119909) = 120596 times 120593 (119909) + 119887 (11)

where 120596 is the weight vector 119887 is error 120593(119909) is a kernel func-tion to deal with the nonlinear problem with mapping thenonlinear input to a high dimensional space by a nonlinearfunction to make the input linear

The least square method in conventional regressionmodel takes the square error as the loss function in accor-dancewithminimizing empirical risks Vapnik et al [44] tookthe 120576-insensitivity as the loss function in SVMmodel and the120576-insensitivity loss is shown as

119871120576(119891 (119909) minus 119910) =

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 ge 120576

0 others(12)

where parameter 120576 determines the area of 120576-insensitivity(Figure 2) When the predicted value 119891(119909) is within the tubearea the loss is zero otherwise the loss is the differencebetween the prediction error and the tube area radius 120576 ℎand ℎ are slack variables indicating the prediction errors indifferent directions

119871120576(119891 (119909) minus 119910) =

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576 = ℎ

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 ge 0

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576 = ℎ

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 lt 0

0 others(13)

where ℎ is the training error which is higher than the areaboundary ℎ is the training error which is lower than the areaboundary

In the input space SVM uses the minimize-adjustment-risk function to calculate the weight vector and the errorThefunction is shown as

119877 (119862) = 1198621

119873

119899

sum

119894=1

119871120576(119891 (119909119894) 119910119894) +

1

21199082

(14)

where 119871120576(119891(119909119894) 119910119894) is the 120576-insensitivity loss function

119862(1119873)sum119899

119894=1119871120576(119891(119909119894) 119910119894) is the empirical error (12)1199082 is

the adjustment itemThen the SVMmodel can be figured outwith minimizing

Min 1

2119908119879

119908 + 119862sum

119894

(ℎ + ℎ)

subject to

119910119894minus 119908119879

119909119894minus 119887 le 120576 + ℎ

119908119879

119909119894+ 119887 minus 119910

119894le 120576 + ℎ

ℎℎ ge 0

(15)

where 119894 = 1 2 119899 is the number of samples for trainingℎ + ℎ is empirical risks (12)119908119879119908 is structure risks whichcan avoid excessive learning119862 is correction factor indicatingthe balance between the experimental risk and the structurerisk Larger 119862 means the model pays more attention to theexperimental risk otherwise more attention to the structurerisk When 119862 120576 and the kernel function 119896 which meetsMercerrsquos condition are determined appropriately the modelcan be solved with Lagrangian multiplier method

Besides in the process of artificial intelligent model con-struction different data will lead to different combinationsof best parameters Therefore the trial-and-error methodis widely used to search the best parameter combinationWith synthetically considering Cherkassky and Marsquos sug-gestions [47] in parameter setting this paper firstly appliesCherkassky and Marsquos method [47] to estimate training datato calibrate several suggested parameter combinations (119862and 120576) of SVM model Then the exponent search method isemployed to select the best parameter combination based onminimizing the mean square error The method can preventthe risk of simple suggested parameter combination and alsoreduce the trial-and-error times

42 Combined Model In this paper wavelet transformdecomposes the original sequence of BDI layer by layer andthen gets a low frequency signal layer and119873 high frequencydetailed layers (119873 is a decomposition level) Fluctuation ofinternational dry bulk shipping market is included in the lowfrequency part of the BDI The impact of random factorssuch as incidents is included in the high frequency part Butthe high frequency part is not an irregular mutational factorTherefore it needs to denoise each layer sequence of low andhigh frequencies respectively A denoised BDI sequence isretained by reconstructing The process of sequence denois-ing not only filters random factors but also makes thepredictive model robust


Wavelettransform

Raw signal data

Low frequency signalL1



High frequency signalH1



middot middot middot

SVR

Inputvector

+Outputvector

k(x1 x)

k(x2 x)

k(xn x)

y1 a1

y2 a2

yn an

Figure 3 Structure of the wavelet transform-SVM combined model

Wavelet transform has characteristics of time-frequencylocalization and zoom features while support vectormachinehas nice tolerance of self-learning adaptive fault general-ization ability and robustness Through operation functionssuch as scaling and translation wavelet transform is ableto analyze functions or signals with multiscale refinementWavelet SVM is combined by the wavelet analysis and SVMcan deal with nonlinear function approximation uniquelyThis research uses wavelet transform to analyze BDI sequenceand then trains the time series by SVM to get trained modelsand predictions Figure 3 shows the structure of hybridforecasting model

5 Case Study

Since 2001 the BDI has experienced a huge fluctuation Thevalue of BDI was less than 1000 points at that time andincreased to more than 11000 points in May 2008 Fivemonths later it decreased to less than 800 points This paper

0

4000

8000

12000

16000

2005

01

04

2006

01

04

2007

01

04

2008

01

04

2009

01

04

2010

01

04

2011

01

04

2012

01

04

BDI

DateBDI

Figure 4 Historical data of monthly averaged BDI (20051ndash201212)

takes data of the BDI published by the Baltic Exchange fromJanuary 2005 to December 2012 as the empirical objectiveBesides the daily BDI data is replaced by month data thatis the objective data is the average BDI for each month


BDI data

Wavelet transform

Low frequencydata L3

High frequencydata H1H2H3

Denoising processing in each layerof the data

Signal reconstruction

Low frequency BDI data

Determine the decompositionscale

The choice of wavelet function

Figure 5 The wavelet transforming process of BDI series

So there are 96 data of BDI Among them the 84 priorconsecutive monthly BDI data are the inputs of the modeland the last 12 monthly BDI data are the outputs of modelThe parameters of the model are selected and the final modelis conformed through SVM training Figure 4 shows thefluctuation phenomenon of monthly data

51 Process Data To avoid the training error resulting fromdimension in sample data or a large dimension data valuethe whole data should be normalized and processed beforethe SVM training Consider

1198781015840

119894= 2 sdot

119878119894minus 119878min

119878max minus 119878minminus 1 (16)

where 1198781015840

119894is normalized value 119878

119894is raw value 119878min is the

minimum value in a sequence of samples 119878max is themaximum value in a sequence of samples

52 Wavelet Analysis The denoising process of original BDIsequence is presented by wavelet transform which is shownin Figure 5 Figure 5 shows the wavelet transform processof BDI series Firstly the raw BDI data split into the highfrequency data and the low frequency data decomposed withthe wavelet transform Then by use of some tech-methodssuch as threshold each sequence will be processed withmanic elimination Go around and around until the final lowfrequency sequence is chosen

Two problems which wavelet function should be selectedin denoising process and how to determine the decompo-sition scale should be solved Different wavelet functionwill get different wavelet transform analysis results which isimportant for the effect of denoising There is no acknowl-edged method about how to choose the optimal waveletfunctions and decomposition scale for signal denoising Sothis paper settles the above two problems with experiment

The purpose of denoising is to remove the mutationfactors and random effects in the sequence So the denoisedsequence should not be too smooth or existing obviousstep phenomenon Considering the orthogonality symmetrysmoothness and other characteristics of thewavelet functionthe best wavelet function and the decomposition scale aredeterminedThe paper used the wavelet toolbox of MATLABto make the test

The commonly used wavelet functions are Haal waveletdbN wavelet symN wavelet biorN wavelet coifN waveletdmey wavelet and so on We make transformation analysisfor the BDI sequence with the same scale and the same ordernumber with different wavelet function This paper will takethree layers of decomposition So the 1119873 is selected as 3After the experience the dbN wavelet is selected as the onein denoising BDI sequence

Then different coefficients of dbN wavelet function areused to analyze wavelet transform The coefficients of dbNwavelet function are usually selected from 1 to 6 Througheffective comparison the coefficient of dbN wavelet functionis settled as 3


600

700

800

900

1000

1100

1200

1300

Pred

icte

d va

lue

Jan Feb Mar Apr May June July Agu Sep Oct Nov DecDate (2012)

BDINeural network (n = 8)

ARMA

Neural network (n = 10)

VARSVR

Figure 6 Forecasting results of four prediction models

53 The Wavelet-SVM to Forecast BDI Sequence The 84prior consecutive monthly BDI data are the inputs of themodel and the last 12 monthly BDI data are the outputs ofmodel The SVM function with output close to the last 12monthly BDI data will be selected The parameters in SVMwhich greatly influence the performance of SVM need tobe optimized and set by users Heuristic algorithms havebeen successfully used in many complex problems [48ndash51]Genetic algorithm (GA) is a common heuristic algorithmwhich has been widely used in lots of literatures [46 52]Therefore GA is also used to optimize the three parameters119862 and 120576 for SVM Due to lots of literatures about GA forreferences [46 52] the process ofGAhas not been introducedin this paper Before the implementation of GA there are fourGA parameters namely 119901

119888 119901119898 119901size and 119879max which need

to be predetermined In general 119901119888varies from 03 to 09 119901

119898

varies from 001 to 01 119901size is the population size which is setaccording to the size of the samples 119879max is the maximumnumber of generation At last after the optimization of GAthe two parameters of SVM were optimized as (55 and 002)with the best optimization value

Then the trained model is presented for one-step predic-tion on the last 12 monthly data To test the forecasting effectof mixed-model three traditional econometric methodsARIMA model VAR model and neural network model areproposed for one-step prediction on the same sample dataSince the above threemodels use the raw BDI sequence as theinput sample for index forecast it has a strong comparabilityCompare the results (Table 2) of one-step prediction with theactual value of BDI For easy understanding and comparingthe actual and predicted values are antinormalized so that thedata back to the realmarket freight index level Figure 6 showsthe compared results of the four predicted models

As can be seen from Figure 6 the predicted resultsobtained from three models have the same trend with theactual value of BDI However among them the deviationbetween the prediction results of neural network and the realvalue is the maximum This is because that the internationaldry bulk market in 2007 and 2008 has always been in volatile

mood causing the artificial neural network falling into theoverlearning problem in the case of small samplesThereforeit amplifies the up and downmagnitude of BDI values for theBDI forecast after 2008 ARMA andVAR itself are suitable forshort-term time series prediction and results are better thanthe neural networkmodel obviously However as can be seenin Figure 6 at some turning points Wavelet-SVM model ismore close to the true value than the ARMA model Table 1shows the forecasting value of each prediction model

This paper uses root mean square error (RMSE) totest training effect and forecasting precision of the variousforecasting methods

RMSE = ( sum

119894=1119873

(119878119891119894minus 119878119903119894)2

119873)

12

(17)

where 119878119903is the actual value of BDI index and 119878

119891is the

prediction valueBy calculating the RMSE of the above four models with

the forecasting result we see that the wavelet-SVM hybridprediction model has the best prediction accuracy The largedeviation among the four models is related with the fall ofBDI under the influence of the economic crisis in 2008 BDIvalue fellmore than 90 frommore than 17000 points inMay2008 to less than 700 points in end of 2008Therefore seeingfrom the predicted trend and the prediction accuracy of eachforecasting model wavelet SVM is the most suitable methodin short-term prediction of BDI

6 Conclusions

Research on the law of shipping market freight fluctuationand the forecasting of the trend of BDI is of special sig-nificance for operators and investors to manage the markettrend and avoid price risk in shipping industry Thereforethis paper constructs awavelet transformand SVMcombinedforecast model It removes the random factors in BDI serieswithwavelet and then establishes a SVMmodelTheBDI datain 2005 to 2012 are presented to test the proposed modelThe 84 prior consecutive monthly BDI data are the inputs ofthe model and the last 12 monthly BDI data are the outputsof model The parameters of the model are selected and thefinal model is conformed through SVM training This papercompares the forecasting result of proposed method withthree other forecasting methods (VARmodel ARMAmodeland neural network) The result shows that the proposedmethod has higher accuracy and could be used to forecastthe short-term trend of the BDI In further research wewill be devoted to improving the prediction accuracy and toforecasting the BDI with long-term period

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper


Table1Fo

recasting

results

offivep

redictionmod

els

BDI

ARM

AVA

RNeuraln

etwork(119899

=8)

Neuraln

etwork(119899

=10)

SVM

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Jan

121039381

9771347

0059888

9251847

0109869

9535296

0082599

9634226

007308

1029505

000

9502

Feb12

702619

6393

836

009

7728565

0099965

7894

652

0123603

7351234

004

6262

6946194

0011385

Mar12

855381

9410

745

0100182

8129358

0049621

8775513

0025919

8762803

00244

338705223

0017701

Apr12

1032905

9806357

00506

049597

050070868

9698

216

0061074

96800

030062837

1090248

0055517

May

12110976

2103637

2006

6132

1221098

0100325

101203

0088066

109227

0015762

111437

8000

416

June

12947

1065348

0124972

1029246

0086849

1072941

0132989

1055275

0114

335

925786

0022401

July12

1064

048

9487609

0108347

95000

950107174

1132184

006

4036

1012775

004

8186

1075023

0010315

Aug12

7635714

7354512

0036827

8435304

0104717

8755779

01466

888220825

0076628

770095

0008543

Sep12

710381

8296

896

016795

682384

0039411

8888169

0251183

8009311

0127467

6901364

0028498

Oct12

944619

1007365

006

6424

1104807

0169579

105953

50121653

1057672

0119

681

9214

623

0024514

Nov12

1021714

9600282

006

0375

1093676

0070432

9599

639

006

0438

1003558

0017771

1010307

001116

5Dec12

8556875

8179

351

004

4119

7999

326

0065158

8113

679

0051794

818812

0043095

8400157

0018315


Table 2 RMSE of the three prediction models

Model RMSEARMA 7896465VAR 9056454Neural network (119899 = 8) 9695657Neural network (119899 = 10) 6597173SVM 2167031

Acknowledgments

The research is sponsored by the National Natural ScienceFoundation of China 51108053 Shandong Natural ScienceFund Project ZR2011GQ011 the Trans-Century Training Pro-gram Foundation for Talents from the Ministry of Educationof China NCET-12-0752 and Liaoning Excellent Talents inUniversity LJQ2012045

References

[1] M G Kavussanos and I D Visvikis ldquoMarket interactions inreturns and volatilities between spot and forward shippingfreight marketsrdquo Journal of Banking and Finance vol 28 no 8pp 2015ndash2049 2004

[2] K Cullinake ldquoA short adaptive forecasting modal for BIFFEXspeculation a Box-Jenkins approachrdquoMaritime Policy amp Man-agement vol 2 pp 91ndash114 1992

[3] J Li and M G Parsons ldquoForecasting tanker freight rate usingneural networksrdquo Maritime Policy amp Management vol 24 no1 pp 9ndash30 1997

[4] K P B Cullinane K J Mason and M Cape ldquoA comparisonof models for forecasting the Baltie Freight Index Box-Jenkinsrevisitedrdquo International Journal of Maritime Economies vol 1no 2 pp 15ndash39 1999

[5] C W J Granger ldquoLong memory relationships and the aggrega-tion of dynamic modelsrdquo Journal of Econometrics vol 14 no 2pp 227ndash238 1980

[6] O T Henry ldquoLong memory in stock returns Some interna-tional evidencerdquoApplied Financial Economics vol 12 no 10 pp725ndash729 2002

[7] N Crato ldquoSome international evidence regarding the stochasticbehavior of stock returnsrdquo Applied Financial Economics vol 4no 1 pp 33ndash39 1994

[8] H W Jonahan ldquoLong memory in emerging stock marketreturnsrdquo Federal Reserve SystemWorking Paper 650 1999

[9] A W Veenstra and P H Franses ldquoA co-integration approachto forecasting freight rates in the dry Bulk shipping sectorrdquoTransportation Research Part A vol 31 no 6 pp 447ndash458 1997

[10] M G Kavussanos and A H Alizadeh-M ldquoSeasonality patternsin dry bulk shipping spot and time charter freight ratesrdquoTransportation Research Part E vol 37 no 6 pp 443ndash467 2001

[11] J Tvedt ldquoA new perspective on price dynamics of the dry bulkmarketrdquo Maritime Policy and Management vol 30 no 3 pp221ndash230 2003

[12] R Adland and K Cullinane ldquoA time-varying risk premium inthe term structure of bulk shipping freight ratesrdquo Journal ofTransport Economics and Policy vol 39 no 2 pp 191ndash208 2005

[13] O Duru E Bulut and S Yoshida ldquoA fuzzy extended DELPHImethod for adjustment of statistical time series prediction An

empirical study on dry bulk freightmarket caserdquo Expert Systemswith Applications vol 39 no 1 pp 840ndash848 2012

[14] H Zhang F Wei and Z Zhang ldquoModeling volatility of balticdry bulk freight indexrdquo in Proceedings of the IEEE InternationalConference on Automation and Logistics (ICAL rsquo08) vol 9 pp1089ndash1094 September 2008

[15] B L Koley and D Dey ldquoAutomatic detection of sleep apneaand hypopnea events from single channel measurement ofrespiration signal employing ensemble binary SVM classifiersrdquoMeasurement vol 46 no 7 pp 2082ndash2092 2013

[16] M G Poddar V Kumar and Y P Sharma ldquoLinear-nonlinearheart rate variability analysis and SVM based classification ofnormal and hypertensive subjectsrdquo Journal of Electrocardiologyvol 46 no 4 p e25 2013

[17] Y CWei and C H Lin ldquoA robust video text detection approachusing SVMrdquo Expert Systems with Applications vol 39 no 12 pp10832ndash10840 2012

[18] X M Chen H B Gong and J N Wang ldquoBRT vehicle traveltime prediction based on SVM and Kalman filterrdquo Journal ofTransportation Systems Engineering and Information Technol-ogy vol 12 no 4 pp 29ndash34 2012

[19] O Duru ldquoA fuzzy integrated logical forecasting model for drybulk shipping index forecasting an improved fuzzy time seriesapproachrdquo Expert Systems with Applications vol 37 no 7 pp5372ndash5380 2010

[20] B Yu and Z Z Yang ldquoAn ant colony optimization model theperiod vehicle routing problem with time windowsrdquo Trans-portation Research Part E vol 47 no 2 pp 166ndash181 2011

[21] W Huang Y Nakamori and S-Y Wang ldquoForecasting stockmarket movement direction with support vector machinerdquoComputers and Operations Research vol 32 no 10 pp 2513ndash2522 2005

[22] K K Seo ldquoAn application of one-class support vector machinesin content-based image retrievalrdquo Expert Systems with Applica-tions vol 33 no 2 pp 491ndash498 2007

[23] B Wohlberg D M Tartakovsky and A Guadagnini ldquoSub-surface characterization with support vector machinesrdquo IEEETransactions on Geoscience and Remote Sensing vol 44 no 1pp 47ndash57 2006

[24] B Yu Z Z Yang K Chen and B Yu ldquoHybrid model forprediction of bus arrival times at next stationrdquo Journal ofAdvanced Transportation vol 44 no 3 pp 193ndash204 2010

[25] B Yu J B Yao and Z Z Yang ldquoAn improved headway-basedholding strategy for bus transitrdquo Transportation Planning andTechnology vol 33 no 3 pp 329ndash341 2010

[26] B YuWHK Lam andM L Tam ldquoBus arrival time predictionat bus stop with multiple routesrdquo Transportation Research PartC vol 19 no 6 pp 1157ndash1170 2011

[27] T van Gestel J A K Suykens D E Baestaens et al ldquoFinan-cial time series prediction using least squares support vectormachines within the evidence frameworkrdquo IEEE Transactionson Neural Networks vol 12 no 4 pp 809ndash821 2001

[28] L J Cao and F E Tay ldquoSupport vector machine with adaptiveparameters in financial time series forecastingrdquo IEEE Transac-tions on Neural Networks vol 14 no 6 pp 1506ndash1525 2003

[29] K J Kim ldquoFinancial time series forecasting using supportvector machinesrdquo Neurocomputing vol 55 no 1-2 pp 307ndash3192003

[30] B Yu B Yu J Lu and Z Z Yang ldquoAn adaptive bus arrival timeprediction modelrdquo Proceedings of the Eastern Asia Society forTransportation Studies vol 7 2009


[31] M Esteban C Arino and J M Dıaz-Cruz ldquoChemometrics forthe analysis of voltammetric datardquo TrAC Trends in AnalyticalChemistry vol 25 no 1 pp 86ndash92 2006

[32] Z Z Yang L J Jin and M H Wang ldquoForecasting BalticPanamax indexwith Support VectorMachinerdquo Journal of Trans-portation Systems Engineering and Information Technology vol11 no 3 pp 50ndash57 2011

[33] P Du K Tan and X Xing ldquoWavelet SVM in ReproducingKernel Hilbert Space for hyperspectral remote sensing imageclassificationrdquo Optics Communications vol 283 no 24 pp4978ndash4984 2010

[34] I Turkoglu and E Avci ldquoComparison of wavelet-SVM andwavelet-adaptive network based fuzzy inference system fortexture classificationrdquoDigital Signal Processing vol 18 no 1 pp15ndash24 2008

[35] G Y Chen and W F Xie ldquoPattern recognition with SVM anddual-tree complex waveletsrdquo Image and Vision Computing vol25 no 6 pp 960ndash966 2007

[36] H Keskes A Braham and Z Lachiri ldquoBroken rotor bardiagnosis in induction machines through stationary waveletpacket transform and multiclass wavelet SVMrdquo Electric PowerSystems Research vol 97 pp 151ndash157 2013

[37] Y Zheng L Zhu and X Zou ldquoShort-term load forecastingbased on Gaussian wavelet SVMrdquo in Proceedings of the 1stInternational Conference on Smart Grid and Clean EnergyTechnologies (ICSGCE rsquo11) pp 387ndash393 September 2011

[38] B Yu Z Yang and S Li ldquoReal-time partway deadheadingstrategy based on transit service reliability assessmentrdquo Trans-portation Research Part A vol 46 no 8 pp 1265ndash1279 2012

[39] V Fernandez ldquoWavelet- and SVM-based forecasts an analy-sis of the US metal and materials manufacturing industryrdquoResources Policy vol 32 no 1-2 pp 80ndash89 2007

[40] Q Wu ldquoThe forecasting model based on wavelet ]-supportvector machinerdquo Expert Systems with Applications vol 36 no4 pp 7604ndash7610 2009

[41] Q Wu and R Law ldquoAn intelligent forecasting model based onrobust wavelet ]-support vector machinerdquo Expert Systems withApplications vol 38 no 5 pp 4851ndash4859 2011

[42] F Y Liu and M Fan ldquoA hybrid support vector machines anddiscrete wavelet transform model in futures price forecastingrdquoin Advances in Neural Networks vol 3973 of Lecture Notes inComputer Science pp 485ndash490 2006

[43] XWangQ Fan C Xu andZ Li ldquoDamdeformation predictionbased on wavelet transform and support vector machinerdquoGeomatics and Information Science ofWuhan University vol 33no 5 pp 469ndash507 2008

[44] V Vapnik M R Muller A J Smola G Ratsch B Scholkopfand J Kohlmorgen ldquoPredicting time series with support vectormachinesrdquo in Artificial Neural Networks vol 1327 of LectureNotes in Computer Science pp 999ndash1004 Springer BerlinGermany 1997

[45] B Z Yao C Y Yang J B Yao and J Sun ldquoTunnel surroundingrock displacement prediction using support vector machinerdquoInternational Journal of Computational Intelligence Systems vol3 no 6 pp 843ndash852 2010

[46] J B Yao B Z Yao L Li and Y L Jiang ldquoHybrid model fordisplacement prediction of tunnel surrounding rockrdquo NeuralNetwork World vol 22 no 3 pp 263ndash275 2012

[47] V Cherkassky and Y Ma ldquoPractical selection of SVM parame-ters and noise estimation for SVM regressionrdquoNeural Networksvol 17 no 1 pp 113ndash126 2004

[48] B Yao C Yang J Hu J Yao and J Sun ldquoAn improved antcolony optimization for flexible job shop scheduling problemsrdquoAdvanced Science Letters vol 4 no 6-7 pp 2127ndash2131 2011

[49] B Z Yao P Hu X H Lu J J Gao and M H Zhang ldquoTransitnetwork design based on travel time reliabilityrdquo TransportationResearch Part C 2014

[50] B Z Yao P Hu M H Zhang and S Wang ldquoArtificial beecolony algorithm with scanning strategy for periodic vehiclerouting problemrdquo SIMULATION Transactions of the Society forModeling and Simulation International vol 89 no 6 pp 762ndash770 2013

[51] B Z Yao P Hu M H Zhang and X M Tian ldquoImprovedant colony optimization for seafood product delivery routingproblemrdquo Promet Traffic amp Transportation vol 26 no 1 pp 1ndash10 2014

[52] A C Lorena and A C P L F de Carvalho ldquoEvolutionarytuning of SVM parameter values in multiclass problemsrdquoNeurocomputing vol 71 no 16-18 pp 3326ndash3334 2008

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


and overreliance on design skills Li and Parsons [3] used theneural network to forecast the tanker freight rate and thencompared with ARMA model They proved that the neuralnetwork model has higher prediction accuracy for a longtime series Cullinane et al [4] forecasted the spot freightrate index with a simple single variable in ARMA modelA new model-fractional integrated autocorrelation movingaverage model (ARFIMA) is presented by Granger [5] indata forecasting Based on the ARFIMA approach Henry [6]showed that almost a half of the new-coming seventeen stockmarkets in the world in the 1990s have long memory whichis similar to their searches by Crato [7] Jonahan [8] and soon

In recent years econometric models are popular infreight rate index forecasting for instance ARIMA modelVAR model and VECM model Empirical analysis showsthat the econometric models have higher accuracy than thetraditional prediction methods for nonstationary time seriesVeenstra andFranses [9] developedVARmodel in forecastingBDI based on cointegrated process of the high time series andthemethod of unit root test Kavussanos andAlizadeh-M [10]presented a single variable seasonalARIMA-SARIMAmodelmultivariable seasonal cointegrating and VAR to analyze theseasonal characteristics of dry bulk shipping market

Tvedt [11] used the unit root tests to reject the randomwalk hypothesis of freight rate confirming a state of sta-tionary in freight rates forecasting for the classical shippingmarket models Two years later a rejection of applicabilityof the expectations theory in freight market was presentedby Adland and Cullinane [12] They also proved that the riskpremium is time varying depending on the freight marketconditions and time charter duration A fuzzy-DELPHIadjustment process for improvement of accuracy was pro-posed by Duru et al [13] They also illustrate its performancein the validation of adjustments of statistical forecasts in theBDI through an empirical study Zhang et al [14] employedRS and GPH tests to model long memory of volatility of theindices based on the investigation of fluctuation features ofdry bulk shipping market with the BDI

A new machine learning method namely support vectormachine (SVM) is widely employed in many fields forinstance handwriting recognition three-dimension objectsrecognition faces recognition text images recognition voicerecognition and regression analysis [15ndash23] The SVM basedon statistical learning theory has good fitting ability forcomplex nonlinear function At the same time it can avoidtrapping problem of overfitting learning A support vectormachine-based (SVM) model is developed to predict thebaseline travel and dwell times of buses based on recent databy Yu et al [24 25] The authors [24 25] also presented ahybrid model based on support vector machine (SVM) andKalman filtering technique to predict bus arrival times Yuet al [26] also adopted support vector machine (SVM) arti-ficial neural network (ANN) 119896 nearest neighborrsquos algorithm(119896-NN) and linear regression (LR) for the bus arrival timeprediction van Gestel et al [27] research the financial timeseries prediction problems based on the least squares SVMmodel Cao and Tay [28] research the parameters of SVMselection and test their approach with empirical analysis of

financial time series The SVM model is widely used in thestock market Kim [29] compared the forecasting result ofstock price index between SVM model with the BP neuralnetwork model and the CBRmodel He proved that the SVMmodel has better prediction of financial time series Huanget al [21] applied SVM to forecast the movement direction ofNIKKEI 225 index

It is suitable for nonlinear time series prediction by theSVM since the full consideration with the randomness ofthe data sequence From the application of SVM especiallyin financial index prediction as well as freight data it is nohard to be employed in another index prediction in terms ofapplicability However SVM is rarely studied and used in thefield of BDI forecast Therefore this paper will analyze theapplicability of SVM model in BDI forecasting and make anempirical test

BDI data sequences can be regarded as signals changedover time The signals usually have characteristics such asperiodic and seasonal of dry bulk shipping market freightindex fluctuationThenoise of the signal reflects the influencefactors of freight index or random events To grasp the ruleof BDI data variation the random disturbance factors shouldbe eliminated Therefore denoising processing of the signalis necessary for an accuracy data forecasting Some methodssuch as a self-adaptive filtration method the Kalman filtermethod and average moving method are often used todenoise signal of data Yu et al [30] adapt an adaptivefiltration method in bus arrival time prediction modelHowever the method of wavelet transform is proposed todenoise the raw signal in this paper

Wavelet transform is the most widely used multiscaleanalysis method till now The root of wavelet transform isscaling and translation in the signal analysis It is a milestonein the history of the development of Fourier analysis In1982 a French oil exploration technician called J Morfettried to deal with irregular signals with wavelet methodmore effectively Research of wavelet analysis was becomingpopular after that It is widely used in image processingvoice processing and signal processing In recent years thewavelet transform method has been employed in areas offinance and economy and the empirical result showed agood effect Esteban et al [31] predicted time series withwaveletmethod Firstly they decomposed the time series intotwo different cycles in sequence with wavelet Then ARMAmodel is present in regression of each data cycle Lastly thetwo forecasting values are added to get the final predictionresults They proved that their proposed approach had betterpredicted result than ARMAmodel

Moreover some researchers also tried to establish thecombined model with the wavelet transform and SVM[32ndash39] Wu [40] proposed novel robust wavelet supportvector machine which is based on wavelet theory and themodified support vector machineThey also designed swarmoptimization algorithm to select the optimal parameters oftheir proposedmodel Two years laterWu and Law [41]madean in-depth research based on the wavelet support vectormachine proposed byWu [40]Wavelet transform is also usedby Guo to map the sample data into several time-frequencydomains He then developed the SVM model to forecast the



















119878 (119905) = 119891 (119905) + 120590119890 (119905) 119905 = 0 1 119899 minus 1 (1)



Original data



High-passseries

Low-passsequence



Denoising data












infin

minusinfin

((119905)2




1205952119895 (119905) =

1

2119895120595(

119905

2119895) (2)



presented as

1198822119895119891 (119905) = 119891 times 120595

2119895 (119905) (3)


forall120596 isin 119877 119860 le

infin

sum

119895=minusinfin

(2119895

120596) le 119861 (2) (4)



infin

sum

119895=minusinfin

(2119895

120596)120594 (2119895

120596) = 1 (5)



2


119891 (119905) =

infin

sum

minusinfin

1198822119895119891 times 120594

2119895 (119905) (6)

119860100381710038171003817100381711989110038171003817100381710038172

le

infin

sum

119895=minusinfin

10038171003817100381710038171198822119895119891 (119905)10038171003817100381710038172

le 119861100381710038171003817100381711989110038171003817100381710038172

(7)



120593(119905)2

=

+infin

sum

119895=1

(2119895

120596)120594 (2119895

120596) (8)


120593(0)2

= lim119896rarr0

(2119896

120596)2

= lim119896rarr0

(2119895

120596)120594 (2119895

120596) = 1

120593(infin)2


(2119896

120596)2


(2119895

120596)120594 (2119895

120596) = 1

(9)



follows1198782119895119891 (119905) = 119891 lowast 120593

2(119905)

1205932(119905) =

1

2119895120593(

119905

2119895)

(10)



2119895119891(119905) but in the



and 2119869 so 119882









denoted by 119878119889119895

2+ 1119891 and 119882

119889119895



shown as follows

119895 = 0while (119895 lt 119869)

119882119889119895

2+ 1119891 = (1120582

119895)119878119889119895

2119891 lowast 119866

119895

119878119889119895

2+ 1119891 = 119878

119889119895

2lowast 119867119895

119895 = 119895 + 1the end


119895 = 119869while (119895 gt 0)

119878119889119895

2+ 1119891 = 120582

119895119882119889119895

2119891 lowast 119870

119895minus1+ 119878119889119895

2119891 lowast 119867

119895minus1

119895 = 119895 minus 1the end

where 119866119895119867119895 and119870



Observer

Observer

Slack variable

Slack variable

Predicted values

Y

X

120576

120576ℏ

ℏ




119891 (119909) = 120596 times 120593 (119909) + 119887 (11)



119871120576(119891 (119909) minus 119910) =

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 ge 120576

0 others(12)


119871120576(119891 (119909) minus 119910) =

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576 = ℎ

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 ge 0

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576 = ℎ

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 lt 0

0 others(13)



119877 (119862) = 1198621

119873

119899

sum

119894=1

119871120576(119891 (119909119894) 119910119894) +

1

21199082

(14)


119862(1119873)sum119899



Min 1

2119908119879

119908 + 119862sum

119894

(ℎ + ℎ)

subject to

119910119894minus 119908119879

119909119894minus 119887 le 120576 + ℎ

119908119879

119909119894+ 119887 minus 119910

119894le 120576 + ℎ

ℎℎ ge 0

(15)





Wavelettransform

Raw signal data








SVR

Inputvector

+Outputvector

k(x1 x)

k(x2 x)

k(xn x)

y1 a1

y2 a2

yn an



5 Case Study


0

4000

8000

12000

16000

2005

01

04

2006

01

04

2007

01

04

2008

01

04

2009

01

04

2010

01

04

2011

01

04

2012

01

04

BDI

DateBDI




BDI data

Wavelet transform











1198781015840

119894= 2 sdot

119878119894minus 119878min


where 1198781015840










600

700

800

900

1000

1100

1200

1300

Pred

icte

d va

lue



ARMA


VARSVR





119898






RMSE = ( sum

119894=1119873

(119878119891119894minus 119878119903119894)2

119873)

12

(17)


119891is the



6 Conclusions





Table1Fo

recasting

results

offivep

redictionmod

els

BDI

ARM

AVA

RNeuraln

etwork(119899

=8)

Neuraln

etwork(119899

=10)

SVM

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Jan

121039381

9771347

0059888

9251847

0109869

9535296

0082599

9634226

007308

1029505

000

9502

Feb12

702619

6393

836

009

7728565

0099965

7894

652

0123603

7351234

004

6262

6946194

0011385

Mar12

855381

9410

745

0100182

8129358

0049621

8775513

0025919

8762803

00244

338705223

0017701

Apr12

1032905

9806357

00506

049597

050070868

9698

216

0061074

96800

030062837

1090248

0055517

May

12110976

2103637

2006

6132

1221098

0100325

101203

0088066

109227

0015762

111437

8000

416

June

12947

1065348

0124972

1029246

0086849

1072941

0132989

1055275

0114

335

925786

0022401

July12

1064

048

9487609

0108347

95000

950107174

1132184

006

4036

1012775

004

8186

1075023

0010315

Aug12

7635714

7354512

0036827

8435304

0104717

8755779

01466

888220825

0076628

770095

0008543

Sep12

710381

8296

896

016795

682384

0039411

8888169

0251183

8009311

0127467

6901364

0028498

Oct12

944619

1007365

006

6424

1104807

0169579

105953

50121653

1057672

0119

681

9214

623

0024514

Nov12

1021714

9600282

006

0375

1093676

0070432

9599

639

006

0438

1003558

0017771

1010307

001116

5Dec12

8556875

8179

351

004

4119

7999

326

0065158

8113

679

0051794

818812

0043095

8400157

0018315




Acknowledgments


References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



























119878 (119905) = 119891 (119905) + 120590119890 (119905) 119905 = 0 1 119899 minus 1 (1)



Original data



High-passseries

Low-passsequence



Denoising data












infin

minusinfin

((119905)2




1205952119895 (119905) =

1

2119895120595(

119905

2119895) (2)



presented as

1198822119895119891 (119905) = 119891 times 120595

2119895 (119905) (3)


forall120596 isin 119877 119860 le

infin

sum

119895=minusinfin

(2119895

120596) le 119861 (2) (4)



infin

sum

119895=minusinfin

(2119895

120596)120594 (2119895

120596) = 1 (5)



2


119891 (119905) =

infin

sum

minusinfin

1198822119895119891 times 120594

2119895 (119905) (6)

119860100381710038171003817100381711989110038171003817100381710038172

le

infin

sum

119895=minusinfin

10038171003817100381710038171198822119895119891 (119905)10038171003817100381710038172

le 119861100381710038171003817100381711989110038171003817100381710038172

(7)



120593(119905)2

=

+infin

sum

119895=1

(2119895

120596)120594 (2119895

120596) (8)


120593(0)2

= lim119896rarr0

(2119896

120596)2

= lim119896rarr0

(2119895

120596)120594 (2119895

120596) = 1

120593(infin)2


(2119896

120596)2


(2119895

120596)120594 (2119895

120596) = 1

(9)



follows1198782119895119891 (119905) = 119891 lowast 120593

2(119905)

1205932(119905) =

1

2119895120593(

119905

2119895)

(10)



2119895119891(119905) but in the



and 2119869 so 119882









denoted by 119878119889119895

2+ 1119891 and 119882

119889119895



shown as follows

119895 = 0while (119895 lt 119869)

119882119889119895

2+ 1119891 = (1120582

119895)119878119889119895

2119891 lowast 119866

119895

119878119889119895

2+ 1119891 = 119878

119889119895

2lowast 119867119895

119895 = 119895 + 1the end


119895 = 119869while (119895 gt 0)

119878119889119895

2+ 1119891 = 120582

119895119882119889119895

2119891 lowast 119870

119895minus1+ 119878119889119895

2119891 lowast 119867

119895minus1

119895 = 119895 minus 1the end

where 119866119895119867119895 and119870



Observer

Observer

Slack variable

Slack variable

Predicted values

Y

X

120576

120576ℏ

ℏ




119891 (119909) = 120596 times 120593 (119909) + 119887 (11)



119871120576(119891 (119909) minus 119910) =

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 ge 120576

0 others(12)


119871120576(119891 (119909) minus 119910) =

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576 = ℎ

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 ge 0

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576 = ℎ

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 lt 0

0 others(13)



119877 (119862) = 1198621

119873

119899

sum

119894=1

119871120576(119891 (119909119894) 119910119894) +

1

21199082

(14)


119862(1119873)sum119899



Min 1

2119908119879

119908 + 119862sum

119894

(ℎ + ℎ)

subject to

119910119894minus 119908119879

119909119894minus 119887 le 120576 + ℎ

119908119879

119909119894+ 119887 minus 119910

119894le 120576 + ℎ

ℎℎ ge 0

(15)





Wavelettransform

Raw signal data








SVR

Inputvector

+Outputvector

k(x1 x)

k(x2 x)

k(xn x)

y1 a1

y2 a2

yn an



5 Case Study


0

4000

8000

12000

16000

2005

01

04

2006

01

04

2007

01

04

2008

01

04

2009

01

04

2010

01

04

2011

01

04

2012

01

04

BDI

DateBDI




BDI data

Wavelet transform











1198781015840

119894= 2 sdot

119878119894minus 119878min


where 1198781015840










600

700

800

900

1000

1100

1200

1300

Pred

icte

d va

lue



ARMA


VARSVR





119898






RMSE = ( sum

119894=1119873

(119878119891119894minus 119878119903119894)2

119873)

12

(17)


119891is the



6 Conclusions





Table1Fo

recasting

results

offivep

redictionmod

els

BDI

ARM

AVA

RNeuraln

etwork(119899

=8)

Neuraln

etwork(119899

=10)

SVM

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Jan

121039381

9771347

0059888

9251847

0109869

9535296

0082599

9634226

007308

1029505

000

9502

Feb12

702619

6393

836

009

7728565

0099965

7894

652

0123603

7351234

004

6262

6946194

0011385

Mar12

855381

9410

745

0100182

8129358

0049621

8775513

0025919

8762803

00244

338705223

0017701

Apr12

1032905

9806357

00506

049597

050070868

9698

216

0061074

96800

030062837

1090248

0055517

May

12110976

2103637

2006

6132

1221098

0100325

101203

0088066

109227

0015762

111437

8000

416

June

12947

1065348

0124972

1029246

0086849

1072941

0132989

1055275

0114

335

925786

0022401

July12

1064

048

9487609

0108347

95000

950107174

1132184

006

4036

1012775

004

8186

1075023

0010315

Aug12

7635714

7354512

0036827

8435304

0104717

8755779

01466

888220825

0076628

770095

0008543

Sep12

710381

8296

896

016795

682384

0039411

8888169

0251183

8009311

0127467

6901364

0028498

Oct12

944619

1007365

006

6424

1104807

0169579

105953

50121653

1057672

0119

681

9214

623

0024514

Nov12

1021714

9600282

006

0375

1093676

0070432

9599

639

006

0438

1003558

0017771

1010307

001116

5Dec12

8556875

8179

351

004

4119

7999

326

0065158

8113

679

0051794

818812

0043095

8400157

0018315




Acknowledgments


References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












infin

minusinfin

((119905)2




1205952119895 (119905) =

1

2119895120595(

119905

2119895) (2)



presented as

1198822119895119891 (119905) = 119891 times 120595

2119895 (119905) (3)


forall120596 isin 119877 119860 le

infin

sum

119895=minusinfin

(2119895

120596) le 119861 (2) (4)



infin

sum

119895=minusinfin

(2119895

120596)120594 (2119895

120596) = 1 (5)



2


119891 (119905) =

infin

sum

minusinfin

1198822119895119891 times 120594

2119895 (119905) (6)

119860100381710038171003817100381711989110038171003817100381710038172

le

infin

sum

119895=minusinfin

10038171003817100381710038171198822119895119891 (119905)10038171003817100381710038172

le 119861100381710038171003817100381711989110038171003817100381710038172

(7)



120593(119905)2

=

+infin

sum

119895=1

(2119895

120596)120594 (2119895

120596) (8)


120593(0)2

= lim119896rarr0

(2119896

120596)2

= lim119896rarr0

(2119895

120596)120594 (2119895

120596) = 1

120593(infin)2


(2119896

120596)2


(2119895

120596)120594 (2119895

120596) = 1

(9)



follows1198782119895119891 (119905) = 119891 lowast 120593

2(119905)

1205932(119905) =

1

2119895120593(

119905

2119895)

(10)



2119895119891(119905) but in the



and 2119869 so 119882









denoted by 119878119889119895

2+ 1119891 and 119882

119889119895



shown as follows

119895 = 0while (119895 lt 119869)

119882119889119895

2+ 1119891 = (1120582

119895)119878119889119895

2119891 lowast 119866

119895

119878119889119895

2+ 1119891 = 119878

119889119895

2lowast 119867119895

119895 = 119895 + 1the end


119895 = 119869while (119895 gt 0)

119878119889119895

2+ 1119891 = 120582

119895119882119889119895

2119891 lowast 119870

119895minus1+ 119878119889119895

2119891 lowast 119867

119895minus1

119895 = 119895 minus 1the end

where 119866119895119867119895 and119870



Observer

Observer

Slack variable

Slack variable

Predicted values

Y

X

120576

120576ℏ

ℏ




119891 (119909) = 120596 times 120593 (119909) + 119887 (11)



119871120576(119891 (119909) minus 119910) =

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 ge 120576

0 others(12)


119871120576(119891 (119909) minus 119910) =

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576 = ℎ

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 ge 0

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576 = ℎ

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 lt 0

0 others(13)



119877 (119862) = 1198621

119873

119899

sum

119894=1

119871120576(119891 (119909119894) 119910119894) +

1

21199082

(14)


119862(1119873)sum119899



Min 1

2119908119879

119908 + 119862sum

119894

(ℎ + ℎ)

subject to

119910119894minus 119908119879

119909119894minus 119887 le 120576 + ℎ

119908119879

119909119894+ 119887 minus 119910

119894le 120576 + ℎ

ℎℎ ge 0

(15)





Wavelettransform

Raw signal data








SVR

Inputvector

+Outputvector

k(x1 x)

k(x2 x)

k(xn x)

y1 a1

y2 a2

yn an



5 Case Study


0

4000

8000

12000

16000

2005

01

04

2006

01

04

2007

01

04

2008

01

04

2009

01

04

2010

01

04

2011

01

04

2012

01

04

BDI

DateBDI




BDI data

Wavelet transform











1198781015840

119894= 2 sdot

119878119894minus 119878min


where 1198781015840










600

700

800

900

1000

1100

1200

1300

Pred

icte

d va

lue



ARMA


VARSVR





119898






RMSE = ( sum

119894=1119873

(119878119891119894minus 119878119903119894)2

119873)

12

(17)


119891is the



6 Conclusions





Table1Fo

recasting

results

offivep

redictionmod

els

BDI

ARM

AVA

RNeuraln

etwork(119899

=8)

Neuraln

etwork(119899

=10)

SVM

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Jan

121039381

9771347

0059888

9251847

0109869

9535296

0082599

9634226

007308

1029505

000

9502

Feb12

702619

6393

836

009

7728565

0099965

7894

652

0123603

7351234

004

6262

6946194

0011385

Mar12

855381

9410

745

0100182

8129358

0049621

8775513

0025919

8762803

00244

338705223

0017701

Apr12

1032905

9806357

00506

049597

050070868

9698

216

0061074

96800

030062837

1090248

0055517

May

12110976

2103637

2006

6132

1221098

0100325

101203

0088066

109227

0015762

111437

8000

416

June

12947

1065348

0124972

1029246

0086849

1072941

0132989

1055275

0114

335

925786

0022401

July12

1064

048

9487609

0108347

95000

950107174

1132184

006

4036

1012775

004

8186

1075023

0010315

Aug12

7635714

7354512

0036827

8435304

0104717

8755779

01466

888220825

0076628

770095

0008543

Sep12

710381

8296

896

016795

682384

0039411

8888169

0251183

8009311

0127467

6901364

0028498

Oct12

944619

1007365

006

6424

1104807

0169579

105953

50121653

1057672

0119

681

9214

623

0024514

Nov12

1021714

9600282

006

0375

1093676

0070432

9599

639

006

0438

1003558

0017771

1010307

001116

5Dec12

8556875

8179

351

004

4119

7999

326

0065158

8113

679

0051794

818812

0043095

8400157

0018315




Acknowledgments


References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Observer

Observer

Slack variable

Slack variable

Predicted values

Y

X

120576

120576ℏ

ℏ




119891 (119909) = 120596 times 120593 (119909) + 119887 (11)



119871120576(119891 (119909) minus 119910) =

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 ge 120576

0 others(12)


119871120576(119891 (119909) minus 119910) =

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576 = ℎ

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 ge 0

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 minus 120576 = ℎ

1003816100381610038161003816119891 (119909) minus 1199101003816100381610038161003816 lt 0

0 others(13)



119877 (119862) = 1198621

119873

119899

sum

119894=1

119871120576(119891 (119909119894) 119910119894) +

1

21199082

(14)


119862(1119873)sum119899



Min 1

2119908119879

119908 + 119862sum

119894

(ℎ + ℎ)

subject to

119910119894minus 119908119879

119909119894minus 119887 le 120576 + ℎ

119908119879

119909119894+ 119887 minus 119910

119894le 120576 + ℎ

ℎℎ ge 0

(15)





Wavelettransform

Raw signal data








SVR

Inputvector

+Outputvector

k(x1 x)

k(x2 x)

k(xn x)

y1 a1

y2 a2

yn an



5 Case Study


0

4000

8000

12000

16000

2005

01

04

2006

01

04

2007

01

04

2008

01

04

2009

01

04

2010

01

04

2011

01

04

2012

01

04

BDI

DateBDI




BDI data

Wavelet transform











1198781015840

119894= 2 sdot

119878119894minus 119878min


where 1198781015840










600

700

800

900

1000

1100

1200

1300

Pred

icte

d va

lue



ARMA


VARSVR





119898






RMSE = ( sum

119894=1119873

(119878119891119894minus 119878119903119894)2

119873)

12

(17)


119891is the



6 Conclusions





Table1Fo

recasting

results

offivep

redictionmod

els

BDI

ARM

AVA

RNeuraln

etwork(119899

=8)

Neuraln

etwork(119899

=10)

SVM

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Jan

121039381

9771347

0059888

9251847

0109869

9535296

0082599

9634226

007308

1029505

000

9502

Feb12

702619

6393

836

009

7728565

0099965

7894

652

0123603

7351234

004

6262

6946194

0011385

Mar12

855381

9410

745

0100182

8129358

0049621

8775513

0025919

8762803

00244

338705223

0017701

Apr12

1032905

9806357

00506

049597

050070868

9698

216

0061074

96800

030062837

1090248

0055517

May

12110976

2103637

2006

6132

1221098

0100325

101203

0088066

109227

0015762

111437

8000

416

June

12947

1065348

0124972

1029246

0086849

1072941

0132989

1055275

0114

335

925786

0022401

July12

1064

048

9487609

0108347

95000

950107174

1132184

006

4036

1012775

004

8186

1075023

0010315

Aug12

7635714

7354512

0036827

8435304

0104717

8755779

01466

888220825

0076628

770095

0008543

Sep12

710381

8296

896

016795

682384

0039411

8888169

0251183

8009311

0127467

6901364

0028498

Oct12

944619

1007365

006

6424

1104807

0169579

105953

50121653

1057672

0119

681

9214

623

0024514

Nov12

1021714

9600282

006

0375

1093676

0070432

9599

639

006

0438

1003558

0017771

1010307

001116

5Dec12

8556875

8179

351

004

4119

7999

326

0065158

8113

679

0051794

818812

0043095

8400157

0018315




Acknowledgments


References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Wavelettransform

Raw signal data








SVR

Inputvector

+Outputvector

k(x1 x)

k(x2 x)

k(xn x)

y1 a1

y2 a2

yn an



5 Case Study


0

4000

8000

12000

16000

2005

01

04

2006

01

04

2007

01

04

2008

01

04

2009

01

04

2010

01

04

2011

01

04

2012

01

04

BDI

DateBDI




BDI data

Wavelet transform











1198781015840

119894= 2 sdot

119878119894minus 119878min


where 1198781015840










600

700

800

900

1000

1100

1200

1300

Pred

icte

d va

lue



ARMA


VARSVR





119898






RMSE = ( sum

119894=1119873

(119878119891119894minus 119878119903119894)2

119873)

12

(17)


119891is the



6 Conclusions





Table1Fo

recasting

results

offivep

redictionmod

els

BDI

ARM

AVA

RNeuraln

etwork(119899

=8)

Neuraln

etwork(119899

=10)

SVM

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Jan

121039381

9771347

0059888

9251847

0109869

9535296

0082599

9634226

007308

1029505

000

9502

Feb12

702619

6393

836

009

7728565

0099965

7894

652

0123603

7351234

004

6262

6946194

0011385

Mar12

855381

9410

745

0100182

8129358

0049621

8775513

0025919

8762803

00244

338705223

0017701

Apr12

1032905

9806357

00506

049597

050070868

9698

216

0061074

96800

030062837

1090248

0055517

May

12110976

2103637

2006

6132

1221098

0100325

101203

0088066

109227

0015762

111437

8000

416

June

12947

1065348

0124972

1029246

0086849

1072941

0132989

1055275

0114

335

925786

0022401

July12

1064

048

9487609

0108347

95000

950107174

1132184

006

4036

1012775

004

8186

1075023

0010315

Aug12

7635714

7354512

0036827

8435304

0104717

8755779

01466

888220825

0076628

770095

0008543

Sep12

710381

8296

896

016795

682384

0039411

8888169

0251183

8009311

0127467

6901364

0028498

Oct12

944619

1007365

006

6424

1104807

0169579

105953

50121653

1057672

0119

681

9214

623

0024514

Nov12

1021714

9600282

006

0375

1093676

0070432

9599

639

006

0438

1003558

0017771

1010307

001116

5Dec12

8556875

8179

351

004

4119

7999

326

0065158

8113

679

0051794

818812

0043095

8400157

0018315




Acknowledgments


References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










BDI data

Wavelet transform











1198781015840

119894= 2 sdot

119878119894minus 119878min


where 1198781015840










600

700

800

900

1000

1100

1200

1300

Pred

icte

d va

lue



ARMA


VARSVR





119898






RMSE = ( sum

119894=1119873

(119878119891119894minus 119878119903119894)2

119873)

12

(17)


119891is the



6 Conclusions





Table1Fo

recasting

results

offivep

redictionmod

els

BDI

ARM

AVA

RNeuraln

etwork(119899

=8)

Neuraln

etwork(119899

=10)

SVM

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Jan

121039381

9771347

0059888

9251847

0109869

9535296

0082599

9634226

007308

1029505

000

9502

Feb12

702619

6393

836

009

7728565

0099965

7894

652

0123603

7351234

004

6262

6946194

0011385

Mar12

855381

9410

745

0100182

8129358

0049621

8775513

0025919

8762803

00244

338705223

0017701

Apr12

1032905

9806357

00506

049597

050070868

9698

216

0061074

96800

030062837

1090248

0055517

May

12110976

2103637

2006

6132

1221098

0100325

101203

0088066

109227

0015762

111437

8000

416

June

12947

1065348

0124972

1029246

0086849

1072941

0132989

1055275

0114

335

925786

0022401

July12

1064

048

9487609

0108347

95000

950107174

1132184

006

4036

1012775

004

8186

1075023

0010315

Aug12

7635714

7354512

0036827

8435304

0104717

8755779

01466

888220825

0076628

770095

0008543

Sep12

710381

8296

896

016795

682384

0039411

8888169

0251183

8009311

0127467

6901364

0028498

Oct12

944619

1007365

006

6424

1104807

0169579

105953

50121653

1057672

0119

681

9214

623

0024514

Nov12

1021714

9600282

006

0375

1093676

0070432

9599

639

006

0438

1003558

0017771

1010307

001116

5Dec12

8556875

8179

351

004

4119

7999

326

0065158

8113

679

0051794

818812

0043095

8400157

0018315




Acknowledgments


References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










600

700

800

900

1000

1100

1200

1300

Pred

icte

d va

lue



ARMA


VARSVR





119898






RMSE = ( sum

119894=1119873

(119878119891119894minus 119878119903119894)2

119873)

12

(17)


119891is the



6 Conclusions





Table1Fo

recasting

results

offivep

redictionmod

els

BDI

ARM

AVA

RNeuraln

etwork(119899

=8)

Neuraln

etwork(119899

=10)

SVM

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Jan

121039381

9771347

0059888

9251847

0109869

9535296

0082599

9634226

007308

1029505

000

9502

Feb12

702619

6393

836

009

7728565

0099965

7894

652

0123603

7351234

004

6262

6946194

0011385

Mar12

855381

9410

745

0100182

8129358

0049621

8775513

0025919

8762803

00244

338705223

0017701

Apr12

1032905

9806357

00506

049597

050070868

9698

216

0061074

96800

030062837

1090248

0055517

May

12110976

2103637

2006

6132

1221098

0100325

101203

0088066

109227

0015762

111437

8000

416

June

12947

1065348

0124972

1029246

0086849

1072941

0132989

1055275

0114

335

925786

0022401

July12

1064

048

9487609

0108347

95000

950107174

1132184

006

4036

1012775

004

8186

1075023

0010315

Aug12

7635714

7354512

0036827

8435304

0104717

8755779

01466

888220825

0076628

770095

0008543

Sep12

710381

8296

896

016795

682384

0039411

8888169

0251183

8009311

0127467

6901364

0028498

Oct12

944619

1007365

006

6424

1104807

0169579

105953

50121653

1057672

0119

681

9214

623

0024514

Nov12

1021714

9600282

006

0375

1093676

0070432

9599

639

006

0438

1003558

0017771

1010307

001116

5Dec12

8556875

8179

351

004

4119

7999

326

0065158

8113

679

0051794

818812

0043095

8400157

0018315




Acknowledgments


References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table1Fo

recasting

results

offivep

redictionmod

els

BDI

ARM

AVA

RNeuraln

etwork(119899

=8)

Neuraln

etwork(119899

=10)

SVM

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Predictvalue

Relativee

rror

Jan

121039381

9771347

0059888

9251847

0109869

9535296

0082599

9634226

007308

1029505

000

9502

Feb12

702619

6393

836

009

7728565

0099965

7894

652

0123603

7351234

004

6262

6946194

0011385

Mar12

855381

9410

745

0100182

8129358

0049621

8775513

0025919

8762803

00244

338705223

0017701

Apr12

1032905

9806357

00506

049597

050070868

9698

216

0061074

96800

030062837

1090248

0055517

May

12110976

2103637

2006

6132

1221098

0100325

101203

0088066

109227

0015762

111437

8000

416

June

12947

1065348

0124972

1029246

0086849

1072941

0132989

1055275

0114

335

925786

0022401

July12

1064

048

9487609

0108347

95000

950107174

1132184

006

4036

1012775

004

8186

1075023

0010315

Aug12

7635714

7354512

0036827

8435304

0104717

8755779

01466

888220825

0076628

770095

0008543

Sep12

710381

8296

896

016795

682384

0039411

8888169

0251183

8009311

0127467

6901364

0028498

Oct12

944619

1007365

006

6424

1104807

0169579

105953

50121653

1057672

0119

681

9214

623

0024514

Nov12

1021714

9600282

006

0375

1093676

0070432

9599

639

006

0438

1003558

0017771

1010307

001116

5Dec12

8556875

8179

351

004

4119

7999

326

0065158

8113

679

0051794

818812

0043095

8400157

0018315




Acknowledgments


References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Acknowledgments


References






























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra







































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article forecasting dry bulk freight index with...

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