On Joint Order and Bandwidth Selection for Identification of Nonstationary Autoregressive Processes

When identifying a nonstationary autoregressive process, e.g. for the purpose of signal prediction or parametric spectrum estimation, two important decisions must be taken. First, one should choose the appropriate order of the autoregressive model, i.e., the number of autoregressive coefficients that will be estimated. Second, if identification is carried out using the local estimation technique, such as the localized version of the method of least squares, one should select the most appropriate estimation bandwidth, i.e., the effective width of the local data window used for the purpose of parameter tracking. The paper presents the first unified treatment of the problem of joint order and bandwidth selection. Two solutions to this problem are examined, first based on the predictive least squares principle, and second exploiting the suitably modified Akaike's final prediction error statistic. It is shown that the best results are obtained if the two approaches mentioned above are combined.