Characterization of the partial autocorrelation function of nonstationary time series

The second order properties of a process are usually characterized by the autocovariance function. In the stationary case, the parameterization by the partial autocorrelation function is relatively recent. We extend this parameterization to the nonstationary case. The advantage of this function is that it is subject to very simple constraints in comparison with the autocovariance function which must be nonnegative definite. As in the stationary case, this parameterization is well adapted to autoregressive models or to the identification of deterministic processes. r 2003 Elsevier Science (USA). All rights reserved. AMS 2000 subject classifications: 60G12; 62M10