Forecasting price of Indian mustard (Brassica juncea) using long memory time series model incorporating exogenous variable

Abstract

The objective of present study was to investigate the efficiency of Autoregressive fractionally integrated moving average model with exogenous input (ARFIMAX) in forecasting price of Indian mustard [Brassica juncea (L.) Czern. & Coss]. The daily modal price and arrival data of mustard for two major markets of India, viz. Bharatpur and Agra were collected during 2008–2018 from AGMARKNET and used for the present investigation. It was observed that each of the price series under consideration is stationary but autocorrelation function of both the series decay in a hyperbolic pattern. This indicates possible presence of long memory in the price data. Moreover, the significant result of correlation between price and arrival indicate that arrival data could be used as exogenous variable to model and forecast the price for both markets. Accordingly, Autoregressive fractionally integrated moving average (ARFIMA) and ARFIMAX models were applied to obtain the forecasts. The forecast evaluation was carried out with the help of Relative mean absolute percentage error (RMAPE) and Root mean square error (RMSE). The residuals of the fitted models were used for diagnosis checking as well as to investigate the adequacy of developed model. To this end, a comparative study has also been made between the fitted ARFIMAX model and ARFIMA model for both in-sample and out-of-sample data to identify the best fitted model in order to forecast future prices. The model has demonstrated a good performance in terms of explained variability and predicting power.

Keywords

• ARFIMA
• ARFIMAX
• correlation
• long memory
• mustard
• stationarity.