Modelling Long Memory Time Series for Groundnut Prices in Andhra Pradesh with Autoregressive Fractionally Integrated Moving Average for Forecasting

Abstract

The presence of long memory in time series is characterized by an autocorrelation function that decreases slowly or hyperbolically. The most suitable model for capturing this phenomenon is the Autoregressive Fractionally Integrated Moving Average (ARFIMA) model, which is particularly useful for modeling historical prices in financial data analysis. This research aims to assess ARFIMA modeling of long memory processes using the Geweke and Porter-Hudak (GPH) parameter estimation method. The model was applied to the monthly prices of Groundnut in Andhra Pradesh, from the period January 2002 to December 2023. The best-fitted model identified was ARFIMA (1,0.43,1), which demonstrates a strong short-term forecasting ability, closely matching actual prices with lowest AIC, MSE and RMSE values when compared to SARIMA(1,1,3)(0,1,2)12 model. The study concluded that the ARFIMA model forecasted better than the SARIMA model for forecasting of Groundnut prices of Andhra Pradesh.