Estimated trend in production of cotton for Ahmedabad district of Gujarat state by statistical models

Abstract

An investigation was carried out using polynomial (linear, quadratic, and cubic) models fitted to the original data as well as three-, four-, and five-year moving-average data. Autoregressive Integrated Moving Average (ARIMA) models were fitted to the original time-series data after checking the stationarity condition, to arrive at a methodology that could precisely explain the fluctuations in cotton production in Ahmedabad district of Gujarat for the period from 1960–61 to 2014–15 (55 years) and to compare different models. The error percentage for the selected model was also calculated to test its prediction power. Data from 1960–61 to 2006–07 were used for model fitting, and the remaining years were used for testing the forecasts. In polynomial models, the most suitable model was selected on the basis of R², significant regression coefficients, root mean square error, mean absolute error, normality (Shapiro–Wilk test), and randomness of residual distribution (Run test). The different ARIMA models (p, d, q) were evaluated on the basis of autocorrelation function (ACF) and partial autocorrelation function (PACF) at various lags. Among the different fitted ARIMA models, the final models were selected on the basis of significant autoregressive and moving average terms, Akaike's Information Criterion (AIC), Schwarz-Bayesian Criterion (SBC), normality (Shapiro–Wilk test), and randomness of residual distribution (Run test). The suitable model for cotton production in Ahmedabad district was ARIMA (1, 1, 0), with the lowest prediction error of 2.602 per cent during 2014–15 and the highest prediction error of 42.036 per cent during 2010–11.