The Kalman filter as an adaptive forecasting procedure for use with Box-Jenkins arima models

Abstract

The Box-Jenkins (BJ) methodology of time series analysis is currently one of the most accurate of the historical approaches to forecasting. It involves the formation of an autoregressive integrated moving average model of the time series. However, there are some important limitations to the procedure: (1) It requires an extensive amount of past observations in order to develop an acceptable model. (2) The model identification process requires a great deal of time and expertise. (3) The model selected is a constant model; there is no convenient way to modify the coefficients with new observations. The research reported here uses the Kalman filter (KF) algorithm to develop a method using an autoregressive moving average model, called “KARMA,” to overcome the three problems mentioned above. The KF estimates the states for dynamic systems in state-variable formulation. The conclusion reached is that the general KARMA method developed in this research can be used to resolve the three main problems associated with the BJ methodology. First, the KARMA model can give good forecasts with fewer data than are required with the BJ. Second, the general model eliminates the need for the model identification process; the only requirement to obtain the forecasts is the time series. Third, the KARMA method is adaptive in the parameters and model.