Reliability in the estimates and compliance to invertibility condition of stationary and nonstationary time series models

摘要

In this paper, we fit models to stationary and non-stationary series for comparison of the estimates of the data, considering invertibility condition for the models. The condition requires that every parameter of a time series model should lie between -1 and 1 exclusive. The distribution of autocorrelation and partial autocorrelation functions as shown Appendixes 1A, 1B, 2A and 2B, suggested AR(1) model for the non-stationary series and ARIMA(2,1,2) for the stationary series. The two models have given good estimates for the series, with residuals which are independently and identically distributed. This paper has established the fact that not until a series is stationary, it becomes invertible. This is affirmation of assertion by Box and Jenkins (1976) that invertibility is independent of stationarity. The models of non-stationary series that are not invertible are those whose data series are absolutely explosive in nature.