02 - 106080

13th Agricultura

lResearch Symposiu

m2014

Department of Agribusiness ManagementFaculty of Agriculture and Plantation Management

Wayamba University of Sri Lanka

Forecasting Paddy Production of Batticaloa District in Sri Lanka:

Linear Time Series Models

L.H.A.M.Silva106080

Content

• Introduction• Objectives• Methodology• Results and Discussion• Conclusion• Acknowledgements• References

IntroductionPaddy– The staple food of Sri Lanka– Contributed 1.6% to the Gross Domestic Production

in year 2013

• Highest paddy producing districts

District Production (t)Ampara 297,229Polonnaruwa 261,263Kurunegala 189,281Anuradhapura 161,406Hambanthota 112,623Batticaloa 111,943

• Batticaloa district – 6th position

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

• Forecasting paddy yield is a challenge

– As the yield depends on• External factors• Internal factors

• Climate has a close relationship with yield

• 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

Objectives

Study was conducted toIdentify accurate linear time series models to forecast paddy production of Batticaloa district

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/

Analysis

• Time series plot

• Trend models– Linear– Quadratic– Exponential Growth– Pearl-Reed Logistic (S-Curve)

• Time Series Models– Single Exponential Smoothing– Double Exponential Smoothing– Winters’ Method– ARIMA Models

• Minitab version 15 was used

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

• Model validationResidual Analysis

–Autocorrelation function of the residual

–Anderson – Darling test

–Run chart

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

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

• A gradual increment after year 2008– May be due to recovery from civil war

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

𝑌 𝑡=106 /(26.3162−(0.592015×1.04193 𝑡))

For Yala Season




Exponential growth trend model

For Maha Season




Pearl-Reed logistic (S curve)

• 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

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

• Adjusting outliers–3 month simple moving average method–Reduced MAPE from 46 to 35

• Residual analysis– Run chart – P value for clustering – 0.806

– Anderson-Darling test – P value obtained 0.262

– Autocorrelation function

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

• Residual analysis– Run chart – P value for clustering – 0.228

– Anderson-Darling test – P value – 0.110

– Autocorrelation function

ConclusionModel MAPE

Single exponential smoothing 64

Double exponential smoothing 69

Winters’ method 35

ARIMA 43.9

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

Acknowledgments

All the academic and non-academic staff members of Faculty of Agriculture and

Plantation Management

References• Agrawal, R., Jain, R. C., Jha, M. P. and Singh, D. (1980) Forecasting

of rice yield using climate variables. In Indian Journal of Agricultural Science, 50(9), 680-684.

• 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.

• 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.

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