Statistical Analysis of Cropland Area in Canada using the Autoregressive Hidden Markov Time Series Model

Abstract

Crop production and other agricultural activities are as old as human existence and becoming increasingly intensive, spatially concentrated and specialized. However, diversification in economic activities and recent development in technology in many developed countries have led to significant increase in land use. Thereby, resulting to huge reduction in the total land area available for agricultural activities especially crop production. This study examines the distribution of cropland area in Canada in relation to three contributing factors using the Autoregressive Hidden Markov time series Model (AR-HMM) due to the limitations of the ordinary Autoregressive model in the accuracy of its parameter estimation. Expectation-Maximization (E-M) algorithm method was used to estimate the model parameters so as to investigate the effects of the factors on cropland distribution using secondary data from Food and Agriculture Organisation (FAO). Jarque-Bera and D'Agostino normality tests were carried out to examine the normality of the series. Augmented Dickey Fuller (ADF) and the KPSS tests established the stationarity of the series. The ideal stationary probability distribution for transition was at AR (3)-HMM with the minimum Bayesian Information Criterion (BIC) of 16270.62. The prior transition states for the HMM are 0.462, 0.260 and 0.278 respectively. In conclusion, this study suggests that deforestation and other land use activities as a result of commercial and technological advancements should be minimized to ensure more available cropland area.