“TREND ANALYSIS OF WHEAT AREA, PRODUCTION AND PRODUCTIVITY IN GUJARAT BY USING STATISTICAL MODELING TECHNIQUES”
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Date
2018-06
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JAU,JUNAGADH
Abstract
Key Words: Shapiro and Wilk test, Run test, polynomial model, ARIMA,
Autocorrelation Function and Partial Autocorrelation Function.The present investigation was carried out on the polynomial (linear, quadratic
and cubic) models were fitted on original data as well as three, four and five year
moving averages data. The Autoregressive Moving Average (ARIMA) models were
fitted to original time series data after checking the stationary condition, to arrive at a
methodology that can precisely explain the fluctuation in area, production and
productivity for wheat crop in different districts is Junagadh, Rajkot, Ahmedabad,
Sabarkantha, Banaskantha and Kheda districts selected from Gujarat state. Gujarat
state to compare different models for the period 1960-61 to 2011-12 (52 years). The
error percentage for the selected model was also carried out to test the prediction
power. The data from year 1960-61 to 2006-07 were used for model fitting and
remaining years for testing the forecast. In polynomial models, the most suitable
model was selected on the basis of adjusted R2, significant regression coefficient, root
mean square error, mean absolute error, normality (Shapiro and Wilk test) and
randomness of residual’s (Run test) distribution. The different ARIMA models (p, d,
q) were judged on the basis of autocorrelation function (ACF) and partial
autocorrelation function (PACF) at various lags. Among different fitted ARIMA
models, the final models were selected on the basis of significant autoregressive and
moving average term, Akaike’s Information Criterion (AIC), Schwartz-Bayesian
Criterion (SBC) and normality (Shapiro-Wilk test) and randomness of residual’s
(Run test) distribution.
Suitable model for wheat area was in Junagadh district was ARIMA (0, 1, 1)
model reveal that the MAPE was found to be considered low (14.19) in the year 2010
the model forecast value was very much close to the actual value, the error was found
to be only 38.02. In compare to area, production and productivity of Junagadh district,
the adjusted R2 were 77%, 78% and 64% respectively. ARIMA (0, 1, 1) model is
found to be better model to forecast. In the Rajkot district area and production
adjusted R2 is 42% and 56% respectively, MAE and MAPE is high (417.74 and 45.9),
ABSTRACT
(1539.97 and 42.26) but in productivity adjusted R2 78% the ARIMA (0, 1, 1) was
found adequate because the MAE and MAPE is low (241.49 and 6.62). The
evaluation of fitted ARIMA model for area, production and productivity in
Ahmedabad district it is ascertained that in all the series none of the model was found
to be adequate the MAPE was not low. They were in the range between ‘25 to 40’.
ARIMA (0, 1, 1) area and production the model is underestimated and productivity
the model over estimated. The adjusted R2 was 10%, 79% and 76% respectively for
Ahmedabad district. Fitted model in the Sabarkantha district area, production and
productivity adjusted R2 77%, 20% and 73% respectively, while it reveals that in
productivity MAPE was found to be low (10.26) and standard error was also low so
this model were forecast future values accurately. Thus ARIMA (1, 1, 1) and ARIMA
(0, 1, 3) were ascertained as the better model for area and productivity of Sabarkantha
district.
In the Banaskantha district for area, production and productivity adjusted R2
was 57%, 71% and 75% respectively the evaluation of fitted ARIMA (2, 1, 0) model
for area that found MAE and MAPE was considerably low (135.03 and 18.95). So
this model can be employed for the forecast. In production the ARIMA (0, 1, 1) was
found very high that MAE and MAPE (595.43 and 30.32). So this model cannot be
employed for forecast purpose and productivity is MAE and MAPE (248.66 and
10.32) this one of the model selection criteria. Thus this model can be employed for
forecast. In the Kheda district area, production and productivity adjusted R2 was 41%,
76%, and 75 respectively, while their area and production is very high in MAPE
(30.91 and 24.42) was found this model is cannot be used to forecast the future values
and productivity of Kheda district ARIMA (0, 1, 1) model was found to be
appropriate for forecasting purpose due to its low MAPE (14.81).
The adjusted R2 value for Gujarat state area, production and productivity
adjusted R2 was is 69%, 77%, and 86% respectively, while there is similarly model of
the ARIMA (0, 1, 1) model was found in the area and productivity was found to be
better model for forecasting as the MAPE given in the (19.39 and 9.58) as compare to
production there is high MAPE (26.93) and this could be not be a better model due to
its high standard error and MAPE. Thus, in general, because of crucial requirement of
model selection criteria in polynomial as well as ARIMA models, few models could
get selected. There is need to examine different techniques for fitted the area,
production and productivity of wheat.
Description
Keywords
AGRICULTURAL STATISTICS