Long Memory Time-series Model (ARFIMA) Based Modelling of Jute Prices in the Samsi Market of Malda District, West Bengal

Abstract

The objective of this paper is modeling and forecasting the weekly jute prices of Samsi market in the Malda district of West Bengal in the presence of long memory process. The long memory behavior of series is investigated by the ACF plot and Hurst R/S analysis. A fractionally integrated autoregressive moving-average (ARssFIMA) model is fitted using 668 weekly data (January 2009-November 2022). This study shows the efficiencies of the Hurst exponent, GPH, Smoothed periodogram, Local Whittle, and Wavelet methods used to estimate the fractional difference parameter in the ARFIMA model. Furthermore, we compared the forecasting abilities of the ARFIMA and ARIMA models. The results show that long memory is present in the jute price series. The models selected according to each method are ARFIMA (3,0.348,0), ARFIMA (3,0.291,1), ARFIMA (2,0.487,0), ARFIMA (3,0.461,0), ARFIMA (2,0.311,0), and ARIMA (2,1,1) on the basis of minimum AIC and BIC using 534 in-sample data. Finally, the wavelet method based ARFIMA (2,0.311,0) model is found to be the best optimal model in terms of MAE, RMSE, and MAPE criteria using 134 out-of-sample data. A comparative study indicates that the forecasting performance of the ARFIMA model is strongly better than that of the ARIMA model in this regard.