We study the performance of two analytical methods and one simulation method for computing in-sample confidence bounds for time-varying parameters. These in-sample bounds are designed to reflect parameter uncertainty in the associated filter. They are applicable to the complete class of...

We study the performance of alternative methods for calculating in-sample confidence and out of-sample forecast bands for time-varying parameters. The in-sample bands reflect parameter uncertainty only. The out-of-sample bands reflect both parameter uncertainty and innovation uncertainty. The...

We introduce a new model for time-varying spatial dependence. The model extends the well-known static spatial lag model. All parameters can be estimated conveniently by maximum likelihood. We establish the theoretical properties of the model and show that the maximum likelihood estimator for the...