This paper is concerned with the adaptive prediction for stochastic processes with abruptly changing parameters modelled as a finite-state Markov chain. The Markov transition matrix is assumed to be known. For the coloured noise disturbance case, it is shown that the optimal prediction algorithm requires a bank of elemental predictors running in parallel with its number growing exponentially with time. If the noise disturbance is white, it is found that the number of the elemental predictors required increases exponentially with the prediction ahead step instead of time. A suboptimal predictor is proposed with substantial reduced storage and computational requirements. Simulation examples show the good performance of the proposed algorithms.
KEY WORDS Stochastic process Markov jump parameter
Minimum square error prediction Adaptive prediction Bayesian approach.
Prediction and forecasting based on time series are important problems in many practical situations and have been extensively studied. If the process parameters are known, the minimum square error predictor is readily calculated (Astrom, 1970; Box and Jenkins, 1970).
The adaptive approaches for processes with unknown, but constant or slowly time-varying parameters have also been developed and found many applications in practice (Beck, 1977;