Dynamic linear models with Markov-switching

This chapter reviews the usefulness of the Kalman filter for parameter estimation and inference about unobserved variables in linear dynamic systems. Applications include exact maximum likelihood estimation of regressions with ARMA disturbances, time-varying parameters, missing observations, forming an inference about the public's expectations about inflation, and specification of business cycle dynamics. The chapter also reviews models of changes in regime and develops the parallel between such models and linear state-space models. The chapter concludes with a brief discussion of alternative approaches to nonlinear filtering.

Chapter 50 State-space models

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Tourism forecasting: accuracy of alternative econometric models

Environmental taxation and unemployment: Some evidence on the ‘double dividend hypothesis’ in Europe

In this article, I first extend the standard unobserved-component time series model to include Hamilton's Markov-switching heteroscedasticity. This will provide an alternative to the unobserved-component model with autoregressive conditional heteroscedasticity, as developed by Harvey, Ruiz, and Sentana and by Evans and Wachtel. I then apply a generalized version of the model to investigate the link between inflation and its uncertainty (U.S. data, gross national product deflator, 1958:1–1990:4). I assume that inflation consists of a stochastic trend (random-walk) component and a stationary autoregressive component, following Ball and Cecchetti, and a four-state model of U.S. inflation rate is specified. By incorporating regime shifts in both mean and variance structures, I analyze the interaction of mean and variance over long and short horizons. The empirical results show that inflation is costly because higher inflation is associated with higher long-run uncertainty.

Unobserved-Component Time Series Models With Markov-Switching Heteroscedasticity: Changes in Regime and the Link Between Inflation Rates and Inflation Uncertainty

Introduction From the point of view of econometric modelling, the Kalman filter is of very little interest. It is simply a statistical algorithm that enables certain computations to be carried out for a model cast in state space form. The crucial point for the econometrician to understand is that the state space form opens up the possibility of formulating models that are much wider and richer than those normally considered. Furthermore, it often allows the setting up of models that have a more natural interpretation and provide more useful information on the nature of underlying economic processes. This second point can be illustrated clearly at the simplest level of a pure time series model. Indeed, the aim of this chapter will be to show how the state space form can be used to provide a framework for modelling economic time series that is in many ways preferable to the more conventional approach based on ARIMA processes. The proposed framework links up closely with that of dynamic econometric models, and the resulting model selection methodology is much more akin to that of econometrics. Perhaps the clearest indication of the closeness of these links is that the starting point for the proposed framework is regression rather than the theory of stationary stochastic processes. The state space form allows unobserved components to be incorporated into a model, and the Kalman filter provides the means of estimating them. The specification of these components must, to some extent, depend on a priori considerations, and since the components presumably have an economic interpretation, the model is a structural one; see Engle (1978). In the reduced form the information on individual unobserved components is not explicitly available since the disturbances that generate the various unobserved components are amalgamated into a single disturbance term. In the case of a linear univariate structural time series model, the reduced form is an ARIMA process.

Andrew C. Harvey

Papers

Advances in Econometrics: Applications of the Kalman filter in econometrics