Models with Time-Varying Mean and Variance: A Robust Analysis of U.S. Industrial Production

Abstract

Many seasonal macroeconomic time series are subject to changes in their means and variances over a long time horizon. In this paper we propose a general treatment for the modelling of time-varying features in economic time series. We show that time series models with mean and variance functions depending on dynamic stochastic processes can be sufficiently robust against changes in their dynamic properties. We further show that the implementation of the treatment is relatively straightforward. An illustration is given for monthly U.S. Industrial Production. The empirical results including estimates of time-varying means and variances are discussed in detail.

Keywords: Common stochastic variance, Kalman filter, State space model, unobserved components time series model

JEL Classification: C22, C51, C53, E23