When has estimation reached a steady state?: The Bayesian sequential test

This paper is concerned with distributions of time series, which (i) are influenced by initial conditions (ii) are stimulated by an exogenous signal or (iii) are obtained by recursive estimation of underlying parameters and thus undergo a transient period. In computer intensive applications, it is desirable to stop the processing when the transient period is practically over. This aspect is addressed here from a Bayesian perspective. Under an often met assumption that the model of a system's time series is recursively estimated anyway, the computational overhead of the constructed stopping rule is negligible. Algorithmic details are presented for important normal ARX models (auto-regression with exogenous variable) and models of discrete-valued, independent, identically distributed data. The latter case provides non-parametric Bayesian estimation of credibility interval with sequential stopping. Copyright (C) 2004 John Wiley Sons, Ltd.