State Space Modelling with Weather as Exogenous Input for Sugarcane Yield Prediction in Haryana
Loading...
Date
2020-05
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
CCSHAU, Hisar
Abstract
Parameter constancy is a fundamental issue for empirical models to be useful for forecasting, analyzing or testing any theory. This work addresses the concept of parameter constancy and the implications of predictive failure. Predictive failure is uniquely a post-sample problem. Unlike classical regression analysis, the state space models are time varying parameters models as they allow for known changes in the structure of the system over time and provide a flexible class of dynamic and structural time series models. The study has been performed in two parts i.e. the development of state space models in two forms (the state space and unobserved component approach), and the state space models with weather as an exogenous input for sugarcane yield prediction in Ambala, Karnal, Kurukshetra, Panipat and Yamunanagar districts of Haryana. The time series sugarcane yield data for the period 1966-67 to 2009-10 of Ambala and Karnal districts, 1972-73 to 2009-10 of Kurukshetra and 1970-71 to 2009-10 of Panipat and Yamunanagar districts were used for the development of different models. The validity of fitted models have been checked for the subsequent years i.e., 2010-11 to 2016-17, not included in the development of the yield forecast models.
The selection of autoregressive orders, i.e., five, three, two, four and five looked reasonable for Ambala, Karnal, Kurukshetra, Panipat and Yamunanagar districts respectively helped in determining the amount of past information to be used in the canonical correlation analysis and further leading to the selection of state vector. Information from the canonical correlation and preliminary autoregression analyses were used to form preliminary estimate of the parameters of state space models and that provided the sugarcane yield estimates using Kalman filtering technique. The UCMs with level, trend and irregular components were fitted to study the trend of sugarcane yield. For all the five districts, the irregular component was found to be highly significant while both level and trend component variances were observed non-significant. Lastly, the state space models with weather as exogenous input using different types of growth trends viz., polynomial splines; PS(1), PS(2) and PS(3) were developed. The weather variables used for each district were selected on the basis of stepwise regression method and PS(2) with weather input was selected as the best suited model for all districts.
The post-sample sugarcane yield estimates were obtained on the basis of fitted SS, UCM and SSM with exogenous input. The predictive performance(s) of the contending models were observed in terms of percent relative deviations and RMSEs of sugarcane yield forecasts in relation to observed yield(s). The SSMs with weather input consistently showed the superiority over SS and UCM models in capturing lower percent relative deviations. Thus, it is inferred that the state space models may be effectively used pertaining to Indian agriculture data, as it takes into account the time dependency of the underlying parameters which may further enhance the predictive accuracy of time-series models with parameter constancy.