Matrix forgetting factor with adaptation

We suggest an approach to provide time-varying parameter estimates in ARMA (Auto Regression Moving Average) models of a stochastic nature based on the use of the recursive version of the Instrumental Variable Method (IVM) wit h a Matrix Forgetting Factor (MFF). We demonstrate that there exists the be st selection of MFF minimizing the error strip bound. This optimal MFF depe nds in a complex manner on a group of unknown parameters. An adaptation pro cedure is suggested to obtain asymptotically this optimal value using only the available measurements. The adaptation procedure is based on one Gaussi an smoothing technique. The combination of IVM with adaptive MFF is a tool for estimating the entries of a non-stationary parameter matrix involved in the ARMA model. An asymptotic analysis of the error matrix is presented. S imulation results demonstrate the effectiveness of the suggested approach.