Detecting and estimating parameter jumps using ladder algorithms and likelihood ratio tests

The problem of recursive identification of autoregressive processes which are subject to parameter jumps of unknown magnitude occurring at unknown times is addressed. A sequential procedure for tracking the parameters, detecting the parameter jumps and estimating the points of change is presented which is based on generalized likelihood ratio (GLR) techniques and application of two adaptive ladder filters: the unnormalized growing memory and sliding memory least squares covariance ladder algorithms. From the prediction error energies which are available from these algorithms, the relevant GLR statistics for detection and location of the parameter jumps is computed and after each jump detection the growing memory ladder algorithm is reinitialized by means of the sliding memory filter estimates.