Asymptotic bias in parameter estimation of AR-processes using recursive least squares with exponential forgetting

The recursive least squares technique is often extended with exponential forgetting as a tool for parameter estimation in time-varying systems. The distribution of the resulting parameter estimates is, however, unknown when the forgetting factor is less than one. In this paper an approximative expression for bias of the recursively obtained parameter estimates in a time-invariant AR(n(a)) process with arbitrary noise is given, showing that the bias is non-zero and giving bounds on the approximation errors. Simulations confirm the approximation expressions.