Forecast Functions Implied by Autoregressive Integrated Moving Average Models and Other Related Forecast Procedures

Abstract

Summary The simplifying operators in ARIMA (autrogressive integrated moving average) models determine the form of the corresponding forecast functions. For example, regular differences imply polynomial trends and seasonal differences certain periodic functions. The same functions also arise in the context of many other forecast procedures, such as regressions on time, exponential smoothing and Kalman filtering. In this paper we describe how the various methods update the coefficients in these forecast functions and discuss their similarities and differences. In addition, we compare the forecasts from seasonal ARIMA models and the forecasts from Winters' additive and multiplicative smoothing methods.