1. Proceedings of 13th
Agricultural Research Symposium (2014)
Forecasting Paddy Production of Batticaloa District in Sri Lanka:
Linear Time Series Models
L. H. A. M. SILVA1
, N. R. ABEYNAYAKE1
and N. K. K. BRINTHA2
1
Department of Agribusiness Management, Faculty of Agriculture and Plantation Management,
Wayamba University of Sri Lanka, Makandura, Gonawila (NWP)
2
Department of Crop Science, Faculty of Agriculture, Eastern University, Sri Lanka
ABSTRACT
Paddy, the staple food of Sri Lankans has contributed 1.6% to the Gross Domestic Product in year
2013. Total paddy production in 2012/2013 Maha season was 2846276 t and in 2013 Yala season was
1774452 t. Ampara, Polonnaruwa, Kurunegala, Anuradhapura, Hambanthota and Batticaloa districts were
the highest contributing districts. Among those Batticaloa district have showed a gradual increase of paddy
production during last few years. Forecasting of paddy production of Batticaloa district is important for
policy makers, farmers, consumers, intermediaries and government for their future planning and decision
making. With this background this study was conducted to identify the trend and appropriate time series
models to forecast paddy production in Batticaloa district. Trend analysis revealed that during early
periods, the production was steady and recent periods the production showed a gradual increase.
Exponential smoothing, Holt-Winters’ method and Autoregressive Integrated Moving Average models were
tested. Mean Absolute Percentage Error was used as the model selection criteria along with the residual
analysis. Winters’ method was selected as the best model to forecast paddy production. The forecast values
of paddy production for the year 2013/14 Maha season was 158695 t, 2014 Yala season was 105481 t and
2014/15 Maha was 213964 t.
KEYWORDS: Forecasting, Paddy production, Time series
INTRODUCTION
Rice is the staple food of Sri Lanka
which has been cultivated since kings’ era.
Paddy cultivation contributed 1.6% to the
Gross Domestic Production of the country
(Anon, 2013). Highest paddy producing
districts and their production in 2013 Yala
season is shown in table 1.
Table 1. Production of highest paddy
producing districts
District Production (t)
Ampara 297,229
Polonnaruwa 261,263
Kurunegala 189,281
Anuradhapura 161,406
Hambanthota 112,623
Batticaloa 111,943
t - tonnes
Batticaloa district is the 6th
highest paddy
producing district in 2013 Yala season.
Although it is a district with large amount of
paddy lands the production was low before
year 2009 due to the civil war. With the end of
civil war in 2009 the paddy production of
Batticaloa district has increased rapidly from
6.2 × 104
t in 2008 Yala season to 11.1 × 104
t
in 2013 Yala season due to expansion of
restricted areas (Anon, 2013).
Thus predicting the paddy production is
important for producers, consumers,
intermediaries and government. Therefore,
forecasting will be useful in planning and
decision making.
However forecasting paddy yield is a
huge challenge as the yield depends on
numerous amounts of external factors such as
weather experienced by the crops, soil
characteristics, amount and quality of the
inputs supplied and internal factors. Among
those factors climate has a closer relationship
with the paddy yield and yield can be
forecasted using the climatic data (De Datta,
1981).
But it is difficult to prepare models
using external factors such as climatic data as
they fluctuate rapidly. Therefore time series
models such as Autoregressive (AR) models,
Moving Average (MA) models,
Autoregressive Moving Average (ARMA)
models and Autoregressive Integrated Moving
Average (ARIMA) models can be used to
forecast paddy yield.
Several studies have been conducted in
different parts of the world as well as in Sri
Lanka to forecast paddy production. Rahman
in 2010 has used ARIMA approach to forecast
Bro rice production in Bangladesh and
Agrawal and his subordinates (1980) have
forecasted paddy production of Raipur district,
Madhya Pradesh, India using climate

2. Silva, Abeynayake and Brintha
variables. Raghavendra (2010) have forecasted
paddy production in Andhra Pradesh using
ARIMA model.
Sri Lankan paddy production was
forecasted by Sivapathasundaram and
Bogahawatte (2012) using ARIMA approach
and Thattil and Walisinghe (2000) have
forecasted paddy production using a mix
model.
But there are no accurate and updated
models to forecast and study the dynamic
behavior of paddy production and models are
unavailable to forecast paddy production in
separate districts. It is also important to update
available models with present data for accurate
forecasting.
With this background this study was
carried out to identify accurate linear time
series models to forecast paddy production of
Batticaloa district in Sri Lanka.
METHODOLOGY
Data Collection
Seasonal time series data from year 1980
to 2013 on paddy production of Batticaloa
district were collected from the official website
of Department of Census and Statistics of Sri
Lanka.
Data Analysis
Time series plot for original data set was
drawn to find out the initial pattern of the data.
Various trend and time series models were
fitted for the data set. Minitab version 15 was
used to analyze the data set.
Trend Models
Linear, Quadratic, Exponential Growth
and Pearl-Reed logistic (S-Curve) trend
models were tested for the paddy production
data to find out the most suitable trend model.
Time Series Models
Single exponential smoothing, double
exponential smoothing, winter’s method and
ARIMA time series models were used to
forecast the paddy production.
Exponential Smoothing
Exponential smoothing models were
fitted to the data set as the first part of the
analysis. Single exponential smoothing gives
the forecast value by adjusting the forecast of
the last period using the forecast error. It can
be expressed as,
( )
Where,
= Observed value for ‘t’ time period
= Fitted value for ‘t’ time period
= Constant between 0 and 1
t = Current time period
Holt, (1957) extended Single Exponential
Smoothing to Double Exponential Smoothing
which allows forecasting of data with trend.
This method consists of three equations. As,
( )( ) (a)
(( ) ( ) (b)
(c)
Two forecasting constants used in double
exponential smoothing, α and β has a value
between 0 and 1. Lt denotes an estimate of the
level of the series at time t and bt denotes an
estimate of the slope of the time series at time
t. Equation (a) adjusts Lt directly for the trend
of the previous period, bt-1, by adding it to the
last smoothed value, Lt-1. This helps to
eliminate the lag and brings Lt to the
approximate level of the current data value.
Equation (b) then updates the trend, which is
expressed as the difference between the last
two smoothed values. This is the appropriate
difference between the last two smoothed
values because if there is a trend in the data,
new values should be higher or lower than the
previous values. Since there may be some
randomness remaining, the trend is modified
by smoothing with β the trend in the last
period, Lt-Lt-1, and adding that to the previous
estimate of the trend multiplied by 1-β. Thus,
equation (b) is similar to the basic form of
single smoothing but applied to the updating of
the trend. Finally equation (c) is used to
forecast ahead. The trend bt, is multiplied by
the number of periods ahead to be forecast, m,
and added to the base value Lt (Wheelwright
and Hydman, 1998).
Holt-Winters’ Method
Holt-winters’ method was fitted to the
data set as the second part of the analysis.
Holt’s method was extended by Winters
(1960) to capture seasonality directly. The
Holt-Winters’ method is based on three
smoothing equations for the level, for trend
and for seasonality. It is similar to Holt’s
method, with one additional equation to deal
with seasonality. There are two different Holt-
Winters’ methods depending on whether
seasonality is modeled in an additive or
multiplicative way.

3. Forecasting Paddy Production of Batticaloa District Sri Lanka
The basic equations for Holt-Winters’
multiplicative model are,
( )( ) (a)
( ) ( ) (b)
( ) (c)
( ) (d)
The basic equations for Holt-Winters’
additive model are as follows. Additive model
is less common when compared to
multiplicative models (Wheelwright and
Hydman, 1998).
( ) ( )( ) (e)
( ) ( ) (f)
( ) ( ) (g)
(h)
Where,
s = Length of seasonality
Lt = Level of the series
bt = Trend
St = Seasonal component
Ft+m = Forecast for m periods ahead
ARIMA Models
As the third section of the analysis
ARIMA models were fitted for the data set.
ARIMA model contains autoregressive and
moving average parameters and differencing in
the formulation of the model which was
introduced by Box and Jenkins in 1970.
Parameters of the ARIMA model are (p, d, q)
where p denotes the autoregressive parameter,
d denotes number of differencing passes and q
denotes moving average parameter.
Model Selection and Validation
Mean absolute percentage error
(MAPE) was selected as the model selection
criterion which was calculated using the
following equation.
∑ | |
Where,
( )
PEt = Percentage error at t time
Yt = Observed value at t time
Ft = Forecasted value at t time
Models with lower MAPE values were
selected as the best models. Residual analysis
was carried out to check the validity of the
selected models.
RESULTS AND DISCUSSION
Average yield for Maha season from year
1980 to 2013 was 84638 t and standard
deviation was 40220 t. Minimum yield of
17105 t for Maha season was obtained in year
1987/1988 and maximum yield of 193274 t
was obtained in year 2009/2010.
Yala season’s production had a standard
deviation of 21164 t and an average of 42920 t.
Maximum yield for Yala season was 111943 t
in year 2013 and minimum yield for Yala
season was 7000 t in year 2007.
For the forecasting purpose, Yala and
Maha seasons were taken together to find out
the seasonal variation of the production
clearly.
The Batticaloa district paddy production
showed a gradual increment after year 2008
(Figure 1). This may be due to the recovery of
the country from the civil war.
Figure 1. Time series plot for paddy
production
Trend Analysis
Discovering suitable trend model for the
data set is important in forecasting process.
The lowest MAPE value was obtained from
the Pearl-Reed logistic (S-curve) trend model
(Table 2) and selected as the best trend model
(Figure 2).
Table 2. MAPE for fitted trend models
Fitted model MAPE Value
Linear 70
Exponential 50
Quadratic 69
Pearl-Reed logistic S curve 49
MAPE – Mean Absolute Percentage Error
( ( ))
Paddy production showed a slight
positive trend before year 2008. But in the
latter parts the paddy production increased
gradually.
2011*2004*1997*1990*19831980
200000
150000
100000
50000
0
Year
Totalproduction(t)
Time Series Plot of Paddy Production

4. Silva, Abeynayake and Brintha
Figure 2. Trend analysis plot for paddy
production
Exponential Smoothing Models
Exponential smoothing forecasts by
assigning exponentially decaying weights from
recent to older observations of a time series.
Best fitted single exponential smoothing model
was α=0.101 and double exponential
smoothing model was α=0.1, ɤ=0.01.
Table 3. Fitted/forecast paddy production in
tonnes
Year Obs.
Fitted/Forecast
values
SES DES
2011-Yala 77196 75363.6 82234.5
2011/12-Maha 171715 75550.5 82454.5
2012Yala 83599 85357.8 92193.7
2012/13-Maha 115630 85178.4 92138.8
2013-Yala 111943 88284.0 95315.9
2013/14-Maha 90696.9 97823.3
2014-Yala 90696.9 98667.9
2014/15-Maha 90696.9 99512.6
MAPE 64 69
SES – Single Exponential Smoothing, DES – Double
Exponential Smoothing, MAPE – Mean Absolute
Percentage Error, Obs. – Observed values
According to MAPE values, Single
Exponential Smoothing model was better for
forecasting paddy production of Batticaloa
district compared to Double Exponential
Smoothing model (Table 3). But there is a
constraint with Single Exponential Smoothing
as it can be used to forecast only one period
ahead.
Holt-Winter’s Trend and Seasonality Model
This method is an extended version of
Double Exponential Smoothing which is able
to capture seasonality directly. Most suitable
Winters’ model obtained was seasonal length-
12 in multiplicative model, α (Level) = 0.8, ɤ
(Trend) =0.01 and Δ (Seasonal) =0.01. Run
chart of resudual proved that residual was
random (P=0.806) and normality of the
residual was revealed by Anderson–Darling
Test (P=0.262). Autocorrelation function of
residual exposed that the resiual was
uncorrelated (Figure 3). Adjusting outliars
helped to reduce the MAPE value from 46 to
35. Values were fitted and forecasted for year
2011, 2012, 2013, 2014 and 2015 using the
model (Table 4).
Figure 3. Autocorrelation function of
residuals
Table 4. Fitted/forecast paddy production in
tonnes
Year-Season Obs.
Fitted /
forecast
values
2011-Yala 77196 61261
2011/12-Maha 171715 152755
2012-Yala 83599 79306
2012/13-Maha 115630 141028
2013-Yala 111943 72627
2013/14-Maha 158695
2014-Yala 105481
2014/15-Maha 213964
2015-Yala 91834
2015/16-Maha 266901
Obs. – Observed values
ARIMA Models
At this stage of the analysis ARIMA
models were fitted by following Box – Jenkins
ARIMA approach. ARIMA (1,1,1) was
selected as the best ARIMA model and
forecasted values for year 2013, 2014 and
2015 was obtained (Table 5). Autocorrelation
function of the residuals proved that the
residuals were uncorrelated (Figure 4) and run
chart revealed that the residuals were random.
Normal distribution of the residuals were
proved by Anderson-Darling test (P=0.110)
and run chart revealed that the residuals were
random (P=0.228). Adjusting outliers helped
to reduce MAPE of the model from 68.8 to
43.9.
2011*
2004*
1997*
1990*
1983
1980
200000
150000
100000
50000
0
Year
Totalproduction(t)
Intercept 37163.4
Asymptote 37999.5
Asym. Rate 1.0
Curve Parameters
MAPE 49
MAD 28424
MSD 1664516064
Accuracy Measures
Actual
Fits
Variable
Trend Analysis Plot for Paddy Production
S-Curve Trend Model
Yt = (10**6) / (26.3162 - 0.592015*(1.04193**t))
161412108642
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
Lag
Autocorrelation
Autocorrelation Function for Residual
(with 5% significance limits for the autocorrelations)

5. Forecasting Paddy Production of Batticaloa District Sri Lanka
Figure 4. Autocorrelation function of
residuals
Table 5. Fitted/forecast paddy production in
tonnes
Year-Season Obs.
Fitted /
forecast
values
2011-Yala 77196 75740.5
2011/12-Maha 171715 51347.7
2012-Yala 83599 64754.1
2012/13-Maha 115630 59543.5
2013-Yala 111943 62423.2
2013/14-Maha 82792.8
2014-Yala 99899.5
2014/15-Maha 91371.9
2015-Yala 97050.1
2015/16-Maha 94855.9
Obs. – Observed values
CONCLUSION
Winters’ Method obtained the lowest
MAPE value for the data set. Thus it can be
used to forecast paddy production of Batticaloa
district accurately than the other models.
According to the forecast values using
selected Winters’ method, paddy production of
Batticaloa district during next two years will
increase significantly if the prevailing
conditions remain.
ACKNOWLEDGEMENTS
Authors express their sincere gratitude to
all the academic and non-academic staff
members of Faculty of Agriculture and
Plantation Management of Wayamba
University for their support.
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1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
Lag
Autocorrelation
Autocorrelation Function of Residual
(with 5% significance limits for the autocorrelations)