ARIMA Algebra

Abstract

Chapter 2 introduces ARIMA algebra. With a few exceptions, this material mirrors the authors’ earlier work. The chapter begins with stationary time series processes – white noise, moving average (MA), and autoregressive (AR) processes – and moves predictably to non-stationary and multiplicative (seasonal) models. Stationarity implies that the time series process operated identically in the past as it does in the present and that it will continue to operate identically in the future. Without stationarity, the properties of the time series would vary with the time frame and no inferences about the underlying process would be possible. A seasonally nonstationary process drifts or trends in annual steps. The “best” seasonal model structure is the one that transforms the series to white noise with the fewest number of parameters.