An adaptive autoregressive model

Abstract

A state space modeling approach for autoregressive integrated-moving average time series is presented. By means of the Kalman filter minimum-variance forecasts can be obtained in real time. The filter is able to recursively adjust its estimates similar to the exponential smoothing algorithms. To speed up the response rate of time series tracking an adaptive filter, which is parallel to the Trigg and Leach adaptive forecasting algorithm, is proposed. Results of computer simulations of the first-order autoregressive adaptive model are shown, using 26 simulated time series. It is seen that the adaptive filter has great potentials for real-time industrial applications.