Forecasting Time Series Allowing for Long Memory and Structural Break

Abstract

Long range dependency or long run persistence is a common issue in agricultural price data. These type of phenomena in time-series process can be modeled with the help of Autoregressive fractionally integrated moving average (ARFIMA) model. The feature often arises when working with real time-series data which might exhibit long memory is the possible presence of structural break in mean or in long memory parameter. In this study, the statistical tests for testing presence of long memory and structural break have been discussed. The joint test (Gil-Alana, 2002) for testing degree of fractional integration and possible presence of structural break at known time epoch is also discussed. Two stage forecasting (TSF) algorithm by Papailias and Dias (2015)is used to obtain the forecasts of a long memory process in presence of structural break. In the present investigation, TSF approach is considered for forecasting daily wholesale price of pigeon pea in Bhopal market of Madhya Pradesh, India. A comparative study of predictive performances has also been carried out among the existing forecasting methodology of a long memory time-series subjected to structural break viz. AR approximation method and AR truncation method. It is concluded that TSF approach outperforms the other methods as far as forecasting is concerned for the series under consideration.