State-Space Models with Regime Switching

Abstract

Both state-space models and Markov switching models have been highly productive paths for empirical research in macroeconomics and finance. This book presents recent advances in econometric methods that make feasible the estimation of models that have both features. One approach, in the classical framework, approximates the likelihood function; the other, in the Bayesian framework, uses Gibbs-sampling to simulate posterior distributions from data. The authors present numerous applications of these approaches in detail: decomposition of time series into trend and cycle, a new index of coincident economic indicators, approaches to modeling monetary policy uncertainty, Friedman's "plucking" model of recessions, the detection of turning points in the business cycle and the question of whether booms and recessions are duration-dependent, state-space models with heteroskedastic disturbances, fads and crashes in financial markets, long-run real exchange rates, and mean reversion in asset returns.

On the stability of Calvo-style price-setting behavior

“…This nonlinearity prevents us from applying apply the standard Kalman filter to evaluate the likelihood of the model. Hence, we exploit the Kim and Nelson (1999) filter for constructing the likelihood. The online appendix provides this technique to evaluate the likelihood and, therefore the posterior distribution.…”

Forecasting realized volatility with changing average levels

“…The solution adopted in this case is the one proposed by Kim (1994) for a state space MS model (see also the many examples provided by Kim & Nelson, 1999). After each step of the Hamilton filter, we collapse the n 2 possible values of µ t at time t into n values, by an average over the probabilities at time t − 1:…”

What drove the mid-2000s explosiveness in alternative energy stock prices? Evidence from U.S., European and global indices

“…We use the Kalman filter technique to estimate the time-varying coefficients. The Kalman filter is a recursive procedure for computing the optimal estimates of the state variables for each period t, conditional on the information set available up to time t (Durbin & Koopman, 2001;Kim & Nelson, 1999). We first estimate the parameters of the model σ ε 2 , σ ν 2 and σ 2 η k via maximum likelihood and then derive the filtered values of the state variables α t and β kt .…”