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TRANSCRIPT
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13th Agricultura
lResearch Symposiu
m2014
Department of Agribusiness ManagementFaculty of Agriculture and Plantation Management
Wayamba University of Sri Lanka
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Forecasting Paddy Production of Batticaloa District in Sri Lanka:
Linear Time Series Models
L.H.A.M.Silva106080
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Content
• Introduction• Objectives• Methodology• Results and Discussion• Conclusion• Acknowledgements• References
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IntroductionPaddy– The staple food of Sri Lanka– Contributed 1.6% to the Gross Domestic Production
in year 2013
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• Highest paddy producing districts
District Production (t)Ampara 297,229Polonnaruwa 261,263Kurunegala 189,281Anuradhapura 161,406Hambanthota 112,623Batticaloa 111,943
• Batticaloa district – 6th position
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Forecasting– Process of making statements about future events
which actual outcomes have not yet been observed
– Forecasting is important to• Government• Policy makers• Intermediaries• Consumers
– For• Planning• Decision making
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• Forecasting paddy yield is a challenge
– As the yield depends on• External factors• Internal factors
• Climate has a close relationship with yield
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• Climate factors such as– Rainfall– Day length– Relative humidity– Temperature
• Climate factors fluctuates rapidly• Lack of continuous & accurate climate data
• One of the best approaches - Time series models
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Objectives
Study was conducted toIdentify accurate linear time series models to forecast paddy production of Batticaloa district
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MethodologyData collection
• Seasonal time series data• From year 1980 to 2013 on paddy production• From official website of Department of Census
and Statisticshttp://www.statistics.gov.lk/
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Analysis
• Time series plot
• Trend models– Linear– Quadratic– Exponential Growth– Pearl-Reed Logistic (S-Curve)
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• Time Series Models– Single Exponential Smoothing– Double Exponential Smoothing– Winters’ Method– ARIMA Models
• Minitab version 15 was used
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Model selection and validation• Model Selection Criteria
Mean Absolute Percentage Error (MAPE)
Where,
PEt = Percentage error at t timeYt = Observed value at t timeFt = Forecasted value at t time
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• Model validationResidual Analysis
–Autocorrelation function of the residual
–Anderson – Darling test
–Run chart
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Results and Discussion
1980/1981
1981/1982
1982/1983
1983/1984
1984/1985
1985/1986
1986/1987
1987/1988
1988/1989
1989/1990
1990/1991
1991/1992
1992/1993
1993/1994
1994/1995
1995/1996
1996/1997
1997/1998
1998/1999
1999/2000
2000/2001
2001/2002
2002/2003
2003/2004
2004/2005
2005/2006
2006/2007
2007/2008
2008/2009
2009/2010
2010/2011
2011/2012
2012/20130
50000
100000
150000
200000
250000
Year
Prod
uctio
n (t
)
Maha season• Maximum (2009/2010) – 193,274 t• Minimum (1987/1988) – 17,105 t
• Average – 84,638 t• Standard deviation – 40,220 t
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19801982
19841986
19881990
19921994
19961998
20002002
20042006
20082010
20120
20000
40000
60000
80000
100000
120000
Year
Prod
uctio
n (t
)Yala season• Maximum (2013) – 111,943 t• Minimum (2007) – 7,000 t
• Average – 42,920 t• Standard deviation – 21,164 t
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• A gradual increment after year 2008– May be due to recovery from civil war
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Trend analysis
Fitted model MAPE Value
Linear 70Exponential Growth 50Quadratic 69Pearl-Reed logistic (S curve) 49
• Best trend model with lowest MAPE
Pearl-Reed logistic (S curve)
For both Yala and Maha seasons
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𝑌 𝑡=106 /(26.3162−(0.592015×1.04193 𝑡))
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For Yala Season
Fitted model MAPE Value
Linear 47Exponential Growth 42Quadratic 44Pearl-Reed logistic (S curve) 43
• Best trend model with lowest MAPE
Exponential growth trend model
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For Maha Season
Fitted model MAPE Value
Linear 50Exponential Growth 48Quadratic 51Pearl-Reed logistic (S curve) 46
• Best trend model with lowest MAPE
Pearl-Reed logistic (S curve)
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• Single exponential smoothing was better than double exponential smoothing
• Single exponential smoothing method can only forecast one period ahead
Exponential smoothing models
Single exponentialsmoothing
Double exponentialsmoothing
α=0.101MAPE = 64
α=0.1, ɤ=0.01MAPE = 69
Time Series Models
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Holt-Winter’s Trend and Seasonality Model (Winters’ method)
• Best fitted Winters’ model– Seasonal length-12–Multiplicative model–α (Level) = 0.8–ɤ (Trend) =0.01–Δ (Seasonal) =0.01
• MAPE = 35• Identification of outliers
– Standardized residual
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• Adjusting outliers–3 month simple moving average method–Reduced MAPE from 46 to 35
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• Residual analysis– Run chart – P value for clustering – 0.806
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– Anderson-Darling test – P value obtained 0.262
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– Autocorrelation function
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ARIMA models• Best fitted ARIMA model
–ARIMA 111• MAPE = 43.9• Identification of outliers
–Standardized residual• Adjusting outliers
–3 month simple moving average method–Reduced MAPE from 68.8 to 43.9
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• Residual analysis– Run chart – P value for clustering – 0.228
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– Anderson-Darling test – P value – 0.110
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– Autocorrelation function
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ConclusionModel MAPE
Single exponential smoothing 64
Double exponential smoothing 69
Winters’ method 35
ARIMA 43.9
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Year-Season Obs. Fitted / forecast values
2011-Yala 77,196 61,2612011/12-Maha 171,715 152,7552012-Yala 83,599 79,3062012/13-Maha 115,630 141,0282013-Yala 111,943 72,6272013/14-Maha 158,6952014-Yala 105,4812014/15-Maha 213,9642015-Yala 91,8342015/16-Maha 266,901
Fitted and forecast values using the Winter’s modelForecast
If the prevailing conditions remain – An increment in paddy production
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Acknowledgments
All the academic and non-academic staff members of Faculty of Agriculture and
Plantation Management
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References• Agrawal, R., Jain, R. C., Jha, M. P. and Singh, D. (1980) Forecasting
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• Anon. (2013). Annual Report (2013). Central Bank of Sri Lanka available from: www.cbsl.gov.lk. (Accessed 28th April 2013).
• De Datta, S.K. (1981). Principles and Practices of Rice Production. John Wiley and Sons, Inc.
• Raghavender, M. (2010). Forecasting paddy production in Andhra Pradesh with ARIMA model. In: International Journal of Agricultural and Statistics Sciences, 6(1), 251-258.
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• Rahman, N.M.F. (2010). Forecasting of bro rice production in Bangladesh: An ARIMA approach. In: Journal of Bangladesh Agricultural University. Available from: http://www.banglajol.info/index.php/jbau/article/download/6406/4901(Accessed 20th March 2014).
• Sivapathasundaram, V., and Bogahawatte, C. (2012). Forecasting of paddy production in Sri Lanka: A time series analysis using ARIMA model. In: Tropical Agricultural Research, 24 (1), 21-30.
• Thattil, R.O., and Walisinghe, W.M.P.K. (2000). Forecasting Paddy Yields. Available from: http://www.goviya.lk/agrilearning/Paddy/Paddy_Research/Paddy_pdf/SE2.pdf. (Accessed 20th June 2014)
• Wheelwright, S. C. and Hydman, R. J. (1998) Forecasting methods and applications. eds. Makridakis, S. European Institute of business administration (INSEAD), 3rd ed. 146 – 169.