Predictive modelling with constant and varying coefficients over time for wheat yield in Haryana
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Date
2017
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CCSHAU
Abstract
Statistics plays an important role in all fields of life and the application of statistical techniques are
numerous. Regression models using time series data occur quite oftenly, however, the assumption of uncorrelated
or independent errors for time series data is often not appropriate. It is common to find response variables which do
not fit the standard assumptions of the linear model. Generalized linear models expand the well-known linear
model to accommodate non-normal response variables. One such extension is the class of varying coefficient
models. In these models, the response variable is allowed to depend linearly on some regressors, with coefficients
as smooth functions of some other predictor variables, called the effect modifiers. A special case of the varying
coefficient model is given for time series data, where the effect modifier variable usually is calendar time and
hence resulting in time-varying coefficient models. The statistical modelling approaches viz., multiple linear
regression, linear discriminant function and linear mixed effects were applied to achieve district-level wheat yield
estimation on agro-climatic zone basis in Haryana. The DOA wheat yield data for the period 1980-81 to 2014-15
of Ambala, Kurukshetra, Rohtak, Karnal, Jind, Sonipat, Gurgaon, Faridabad, Mahendragarh, Hisar, Sirsa and
Bhiwani districts, 1989-90 to 2014-15 of Yamunanagar, Panipat, Kaithal and Rewari, 1995-96 to 2014-15 of
Panchkula, 1997-98 to 2014-15 of Jhajjar and Fatehabad and 2006-07 to 2014-15 of Mewat district(s) were used in
obtaining trend yield. The fortnightly weather data of Hisar, Ambala, Karnal, Rohtak, Gurgaon and Bawal were
used for the purpose. The zonal wheat yield forecast models have been developed on the basis of time-trend and
weather data from 1980-81 to 2009-10 while the data from 2010-11 to 2014-15 were used for validation of the
developed models. Yield/time variables were included to take care of variation between districts within zone as the
weather data were not available for all the districts, though the zonal model utilized the same weather information
in adjoining districts under the zone so that a longer series could be obtained in a relatively shorter period and that
also provided the basis to use advanced statistical techniques.
For quantitative forecasting, zonal wheat yield models were fitted by taking fortnightly weather data
(regression analysis) and discriminant/weather scores (discriminant analysis) along with trend yield as regressors
and DOA wheat yield as regressand. Alternatively, the linear mixed effects models with random time effects at
district and zone level and random time/weather effects at intercept with different covariance structure were tried.
The performance of fitted models were decided on the basis of statistic(s) like AIC, BIC and log likelihood etc..
The predictive performance(s) of the contending models were observed in terms of percent deviations of wheat
yield forecasts in relation to the observed yield(s) and root mean square error(s) as well. The linear mixed effects
i.e. varying coefficients models performed well with lower error metrics as compared to the alternative models in
most of the time regimes. Five-steps ahead forecast figures i.e. 2010-11 to 2014-15 favour the use of varying
coefficient models to obtain pre-harvest wheat yield prediction in Haryana. The overall results indicate the
preference of using varying coefficients models in comparison to conventional i.e. constant coefficients models for
this empirical study. In addition, the developed models are capable of providing the reliable yield estimates well in
advance of the crop harvest while on the other hand, the DOA yield estimates are obtained quite late after the
actual harvest of the crop.
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