Efficient Estimation of the Parameter Path in Unstable Time Series Models

Abstract

The paper investigates inference in nonlinear and non-Gaussian models with moderately time varying parameters. We show that for many decision problems, the sample information about the parameter path can be summarized by an artificial linear and Gaussian model, at least asymptotically. The approximation allows for computationally convenient path estimators and parameter stability tests. Also, in contrast to standard Bayesian techniques, the artificial model can be robustified so that in misspecified models, decisions about the path of the (pseudo-true) parameter remain as good as in a corresponding correctly specified model.

Keywords: Time Varying Parameters, Non-linear Non-Gaussian Smoothing, Weighted Average Risk, Weighted Average Power, Posterior Approximation, Misspecification

JEL Classification: C22, C13, C12, C11