Forecasting an explosive time series

Forecasting is an important exercise in Time series analysis. For a statio-nary time series, there are theoretically strong forecasting methods which canprovide most accurate forecasts for the future (Karlin and Taylor (1975)).For most non stationary time series Box Jenkins methodology is a usefulforecasting technique. Essentially, the Box Jenkins methodology assumesthat any non stationarity time series can be conveniently modeled as anAutoregressive Intregrated Moving Averages (ARIMA) model with sucientnumber of unit roots in the linear stochastic dierence equation generatingthe time series. The non stationarity in such time series is then removed bysuccessively dierencing of the series until one obtains a stationary series,for which optimal forecasts can be computed. The forecasts for the originalseries are then computed by 'inverting' the dierence operators that wereused ( Makridakis et al. (1998)) on the forecasts computed for the statio-nary series. The main objective of this study is to demonstrate that the BoxJenkins methodology is not useful, especially in large time series, when thenon stationarity in the time series is due to 'explosive' roots. An alternativemethod is proposed in such a situation and its performance is assessed bothon a simulated as well as on a real life data.