equity journal of science and technology, 2016, 4(1): 86

Equity Journal of Science and Technology, 2016, 4(1): 86-92ISSN: 2354 - 1814

An Official Publication of Kebbi State University of Science and Technology, Aliero Nigeria.EQUIJOST

EVALUATING ARIMA MODELS FORECAST ON THE CURRENT ACCOUNT DEFICIT IN NIGERIA USING SYMMETRIC LOSS FUNCTIONS

?1 1 1Lawal, H., Ahmed, A., Tasi'u, M.

1* Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria

*Corresponding author's email address:

ABSTRACTThis study sought to evaluate the prediction ability of ARIMA models on the current account deficit in Nigeria using symmetric loss functions like Mean Absolute Error (MAE), Root Mean Absolute Error (RMAE), Mean Absolute Percentage Error (MAPE) and Theil inequality Coefficient. The results of the unit root tests show that the data is stationary at lag 3 after taking the first difference of the series. Of two possible models, ARIMA (2,1,2) model is found to be the best model because it has lower AIC and BIC. The accuracy of volatility forecast of the two models were evaluated using the above symmetric loss functions and the results show that ARIMA (2,1,2) produces the most accurate forecast as it has least variance and maximum covariance proportions.

Keywords: ARIMA, Current Account Deficits,Symmetry Lost Functions

1.0 INTRODUCTIONNigeria, like most developing countries, adopted stabilization and adjustment policies in the early 1980s. These programs of reforms were attempts to move the country away from regulated market to a more friendly market oriented economy. This is because of the perception of policy-makers that the adoption of the neo-classical economic doctrine is capable of propelling the economy to the path of sustained growth and development, and therefore addresses the adverse changes in current account. In line with this conceptualization of reform, Nigeria has adopted various forms of policies and institutional reforms since independence Udah [1].

These range from protectionism and excessive government control of economic activity to movement towards free market economy. The era of free market economy started in 1986 when there was a major policy shift. Prior to the introduction of economics of laissez faire in early 1986, which resulted to the adoption of the Structural Adjustment Programme (SAP), the Nigerian economy was characterized by excessive government control of production, financial intermediation processes and foreign trade variables via the administrative determination of interest rates, prices and exchange rate of the naira vis-à-vis other currencies.

To further boost the domestic economy, various economic and structural reforms were introduced in 2003 under a comprehensive economic blue print named the National Economic Empowerment and

Development Strategy (NEEDS). NEEDS sets out to build and promote comprehensive macroeconomic policies and non policy factors that would support economic growth and development and a healthy external account position. In spite of these various reforms in macroeconomic management, the country has continued to run a considerable current account deficit. As a ratio to Gross Domestic Product (GDP), current account deficits have frequently exceeded the five per cent benchmark. In particular, in 1977 the current account stood at three per cent of GDP and increased to 10 per cent in 1978, and peak at 15 per cent in 1982. Albeit most parts of the 1980s witnessed a favourable current account situation, this was short lived as the current account plunge back to deficit in 1993. Current account deficits reached 8 per cent in 1995 and 10 per cent in 1998 Udah [1].

External sector performance improved substantially in 2000 as the overall balance of payments swung from a deficit of over #32 million in 1999, to a surplus of over #31 million naira. The favorable development was attributed to the improvement in the current account. In 2002, the current account returns to the path of deficit before maintaining surplus from 2003 to 2008. This oscillation in current account balance in the past decades despite reforms aimed at addressing it is a major problem of this research and has triggered question as to how macroeconomic, structural and non policy variables determine current account behavior. Understanding which of these variables influence current account behavior positively provides menu of choices for policy makers in addressing adverse

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changes in current account movement in Nigeria. The objective of this study is to investigate which of these factors could be used by policy makers to address adverse changes in current account behavior in Nigeria. To achieve the objective of this paper four sets of hypothesis are developed namely, macroeconomic variables addresses adverse changes in current account; monetary variables are important in explaining current account behavior; structural features or stage of development and external factors reduces adverse changes in current account behavior in Nigeria. Udah [1].

1.1 A Relation for Calculating Current Accounts

A country's current account can be calculated by the following formula:

(1)

Where CA is the current account, X and M the export and import of goods and services respectively, NY the net income from abroad, and NCT the net current transfers.

1.2 Literature Review and Conceptual Issues

The current account is the mirror image of the sum of the capital and financial accounts. One might then ask: Is the current account driven by the capital and financial accounts or is it vice versa? The traditional response is that the current account is the main causal factor, with capital and financial accounts simply reflecting financing of a deficit or investment of funds arising as a result of a surplus. However, more recently some observers have suggested that the opposite causal relationship may be important in some cases. In particular, it has controversially been suggested that the United States current account deficit is driven by the desire of international investors to acquire U.S. assets (See Ben Bernanke, William Poole links http://www.federalreserve.gov/boarddocs/speeches/2005/200503102/). However, the main viewpoint undoubtedly remains that the causative factor is the current account and that the positive financial account reflects the need to finance the country's current account deficit. The Budget deficit and trade deficit i.e. twin deficit have very important role in any economy. Many recent studies argue in favor of the close relationship between the twin deficits i.e. the Keynesian proposition see Darrat [2], Abell [3], Zietz and Pemberton [4], Vamvoukas [5]. While the others economist like Dewald and Ulan [6], Enders and Lee [7] and Kim [8] were in support of the Ricardian equivalence that the relationship between the budget

deficit and trade deficit is not correlated.

The problem of twin deficits has been one of the most disputed issues in economics. Different schools of thoughts have different ideas about the relationship between budget deficits and current account deficits in both developed and developing countries. The study of twin deficit phenomena got serious attention from researchers due to the reason that in most of the situation, twin deficits may lead to economic harms and hurt economic growth. The link between an economy's current account deficit and its budget deficit delighted wide academic debate and empirical testing over the decades.

Researchers such as Kawai [9], Hutchison and Charles [10] and Vamvoukas [5]found support for the conventional view that a worsening budget deficit stimulates an increase in current account deficit. According to Hutchison and Charles [10] an increase in the budget deficit is likely to raise domestic real interest rates and subsequently would increase the trade deficit. They are plethora of literature on the determinants of current account behavior. Baharumshah, et al. [11] investigated the twin deficit hypothesis in Indonesia, Malaysia, the Philippines and Thailand. They found a long run relationship between budget deficit and current account. Their results also showed a unidirectional causality, which runs from budget deficit to current account deficit for Thailand. In Indonesia, current account targeting was detected, whereas in Malaysia and Philippines, the causality was bidirectional. Chete [12] found a negative correlation between current account and variables such as square of relative income, inflation, the degree of openness in Nigeria. His study also showed the existence of a positive relationship between current account balance and net foreign assets, budget deficit and exports. Ozman [13]empirically investigated the effects of institutional and macroeconomic policy stance variables on current account deficits. The results strongly suggest that better governance increases the ability of a country to control adverse changes in current account behavior. In addition, the findings of the paper indicated that a flexible exchange rate and openness imposes a discipline on current account behavior. The net impacts of the financial deepening and monetary credibility on current account balance were found to be insignificant. Henry and Longmore, [14] investigated the current account dynamics and exchange rate behavior in Jamaica. They found that changes in real exchange rate have significant impact on economic activity by altering the relative returns in the tradable and non-tradable sectors. They however did not find any significant relationship between current account and exchange rate.

Lawal and Ahmed : Evaluating Arima models forecast on the current account deficit in Nigeria using symmetric loss functions

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Zamanzadeh and Mehrara [15] found long run association between current government budget deficits on non-oil current account deficit of Iran for the data related to 1959-2007 through co-integration technique. The variables used in this study include gross domestic product, non-oil export, aggregate import, government consuming expenditures and government tax revenue. A bidirectional causal relationship was also witnessed. So estimated long run coefficient confirms Keynesian's view or existence of twin deficits in the Iranian economy. Aqeel and Nishat [16] suggested that budget deficit has powerful long run effects on current account deficit in Pakistan. No relationship was found between the twin deficits through the interest rate relationship and no co-integration between interest rate and the twin deficits was found. The long run effect of current account deficit on budget shortfall was positive. There was also no evidence of short run causality from current account balance to fiscal deficit. Hakro [17] used vector autoregressive model on time series data from 1948 to 2005, reveal the causal relationship between twin deficits and other macroeconomic variables in Pakistan. The model suggested that changes in interest rates are not responsible for the prior changes in budget and trade deficits. A descriptive review of Mexico's recent economic history indicates that deficits in its current account can be corrected through economic policy; e.g., current account deficits in Mexico are not sustainable (Hutchison and Charles [10]). The objective of this study is to evaluate ARIMA models forecast on the current account deficit in Nigeria using symmetric loss functions

2.0 MATERIALS AND METHODS

2.1 Introduction

Time domain is usually explicitly parametric in nature and are based on direct modeling of the lagged relationship between a series and its past history possibly to forecast its future value. The models for time series that are required to achieve optimal prediction and possible control are stochastic models. These models are used to calculate the probability of future values falling between upper and lower units specified. It is often necessary to distinguish between the probability model or stochastic process and the observed time series. For a single time series, the most widely applied time domain models are based on the so called auto-aggressive integrated moving average (ARIMA) models.

2.2 Data and Software used in the Study

The data used in this study is the weekly current

account deficit of Nigeria spanning from 1996, 29th January to 2013, 30th September, collected from the Central Bank of Nigeria Statistical Bulletin. Total sample of size 925 observations were used for the analysis and 625 observations were used as out-sample to validate the accuracy and adequacy of the models. Statistical software, Gretl (Gnu Regression and Econometrics Library), version 1.9.2cvs was used for the data analyses.

2.3 Auto Regressive Integrated Moving Average (ARIMA) of order (p,d,q) A time series process (y ) is said to follow ARIMA t

(p,d,q) if it has the following representations,

2.4 Kwiatkowski, Philips, Schmidt and Shin KPSS (1992)Proposed a test of the null hypothesis that an observation series is trend stationary (stationary around a deterministic trend).The integrated properties of a series may also be integrated by testing the null hypothesis that the series is stationary against a unit root. Assuming no linear trend error the data generating process is given as;

2.5 Augmented Dickey Fuller (ADF) TestThe ADF regression equation due to Dickey and Fuller [19] and Said and Dickey [20] is given by


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2.6 Symmetric Loss FunctionsSymmetric functions are used to quantify the variability performance of some models or to compare several models, we should define error functions. The following are the most used error functions:

different models; the smaller the error, the better the forecasting ability of that model according to that criterion. The inequality coefficient always lies between zero and one, where zero indicates a perfect fit.

Note also that the mean squared forecast error can be decomposed as:

The bias proportion tells us how far the mean of the forecast is from the mean of the actual series. The variance proportion tells us how far the variation of the forecast is from the variation of the actual series. The covariance proportion measures the remaining unsystematic forecasting errors.Note that the bias, variance, and covariance proportions add up to one.If your forecast is “good”, the bias and variance proportions should be small so that most of the bias should be concentrated on the covariance proportions.

3.0 RESULTS AND DISCUSSION3.1 Data PropertiesFigure 3.1 indicates that the series contains trend components. To remove the trend components, we take the first difference (d) of the logarithms (I) of the data and the series are preferred in analysis of financial time series because they have attractive statistical property which is stationarity as shown in figure 3.2.


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(7)

(8)

=

=

(10)

(5)=

(9)

3.2 Unit Root TestTable 3.1: Results of KPSS and ADF Test Statistics

The ADF and KPSS tests confirm the stationary of the series since there is no unit root. i.e, value of the test statistic for KPSS is less than all the alpha values and greater than those in ADF test.

3.3 Model IdentificationSearching with the aid of information criterion, we resolved at the ARIMA (3,1,3) and ARIMA(2,1,2) as the parsimonious models, with minimum AIC, SIC and

HQC, as it is common in modeling. The table below shows how the models were arrived at.

3.4 Model EstimationThe parameters of the models selected are now estimated in the table below:

The above table shows that ARIMA (2,1,2) is the best model because it has lower AIC and BIC.


90

800

700

600

500

400

300

200

100

1996 1998 2008 2002 2004 2006 2008 2010 2012 20140

Fig. 3.1: Time plot for Nigerian current account deficit

200

150

100

0

50

1998 2000 2002

-50

-100

-1501996

Year2008 2010 2012 20142004 2006

Figure 3.2: First Difference of Logarithm for Nigerian current account deficit

3.5 Forecast EvaluationGood ARIMA models have the ability to forecast and capture the feature values of the security in consideration. To further testify the validity of such models, accuracy of their volatility forecasts are measured using symmetric loss functions such as Mean Absolute Error (MAE), Root Mean Absolute Error (RMAE), Mean Absolute Percentage Error (MAPE) and Theil inequality Coefficient.

Table 3.3: Comparison of the Accuracy of Volatility Forecasts

The results (Table 3.3) of the out-of-sample comparisons of accuracy of forecasts show that ARIMA (2,1,2) model provide the most accurate forecasts for future account deficit of the country. Because it has least variance and maximum covariance proportions.

4.0 CONCLUSIONThe main goal and advantage of time series is forecasting in advance what may happen in the future. From the results of the analysis, the data is stationary at lag 3 after the first difference which was verified using unit root tests (KPSS and ADF tests) at 1%, 5% and 10% level of significance. Of two possible ARIMA models fitted, ARIMA (2,1,2) is selected as the best model passing the information criteria. The parameters of the two models are all statistically significant at 5% level with exception of the constants. In order to evaluate the accuracy of volatility forecast of the two models, symmetric loss function like MAE, RMSE, MAPE among others were used and the results show that ARIMA (2,1,2) produces the most accurate forecast.

REFERENCES[1]. Udah, E. B. 2011: Adjustment Policies and Current Account Behaviour: Empirical Evidence from Nigeria. European Journal of Humanities and Social Sciences. 6 (1), 217-231.

[2]. Darrat, A. F. 1988: Have Large Budget Deficits Caused Rising Trade Deficit? Southern Economic Journal. 54: 879-87.

[3]. Abell, J. D. 1990: Twin Deficits During the 1980's:

An Empi r i ca l Inves t iga t ion . Journa l o f Macroeconomics. 12: 81-92.

[4]. Zietz, J. and Pemberton, D. K. 1990: The US Budget and Trade Deficits: A Simultaneous Equation Model, Southern Econ. J. 57: 23-34.

[5]. Vamvoukas, G. 1999: The Twin Deficits Phenomenon: Evidence from Greece. Applied Economics. 31: 1093-1100.

[6]. Dewold, W. G. and Ulan, M. 1990: The Twin-Deficit Illusion. Cato Journal. 10: 689-707.

[7]. Enders, W. and Lee, B. S. 1990: Current Account and Budget Deficits; Twin or Distant Cousins? The Review of Economics and Statistics. 72: 373-81.

[8]. Kim, K. H. 1995: On the Long-run Determinants of the US Trade Balance: a Comment. J. of Post Keynesian Econ.. 17: 447-55.

[9]. Kawai, M. 1985: Exchange Rates, the Current Account and Monetary - Fiscal Policies in the Short Run and in the Long Run. Oxford Economic Papers. 37: 391-425.

[10]. Hutchison, M. M. and Charles, P. 1984: Budget Deficits, Exchange Rates and the Current Account: Theory and U.S. Evidence. Federal Res. Bank of San Francisco. Econ. Review. 5-25.

[11]. Baharumshal, A. Z., Lau, E. and Ichalid, A. M. 2000: Testing Twin Deficits Hypothesis: Using VAR a n d V a r i a n c e D e c o m p o s i t i o n . [email protected]

[12]. Chete, L. N. 2001: Explaining Current Account Behaviour in Nigeria. The Nigerian J. of Economic and Social Studies. 43: 219-238.

[13]. Ozmen, E. 2004: Current Account Deficits, Macroeconomic Policy Stance and Governance: An Empirical Investigation. ERC Working Papers in Economics.

[14]. Henry, C. and Longmore, R. 2003: Current Account and the Real Exchange Rate Dynamics. The Jamaican Experience', Bank of Jamaica Working Papers.

[15]. Zamanzadeh, A. and Mehrara, M. 2011: Testing Twin Deficits Hypothesis in Iran Interdisciplinary J. of Res. in Bus. 1(9): 07-11.

[16]. Aqeel, A. and Nishat, m. 2000: The Twin Deficits Phenomenon: Evidence from Pakistan.


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The Pakistan Deve. Review. 39(4): 535-550.

[17]. Hakro, A. N. 2009). Twin Deficits Causality Link-Evidence from Pakistan. International Res. J. of Finance and Econ., 24: 54-70.

[18]. Kwiatkowski, D., Phillips, P.C.B. Schmidt, P. and Y. Shin, P. 1992: Testing the null of stationarity against the alternative of a unit root, Journal of Econometrics, 54:159178.

[19]. Dickey, D. A. and Fuller, W. A. 1979: Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association. 74: 427-431.

[20]. Said, S. E. and Dickey, D. A. 1984: Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika,71: 599-60.


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