We show that the covariance function of a second-order stationary vector Markov regime switching time series has a vector ARMA(p; q) representation, where upper bounds for p and q are elementary functions of the number of regimes. These bounds apply to vector Markov regime switching processes with both mean-variance and autoregressive switching. This result yields an easily computed method for ...

This paper develops a new econometric framework for investigating how the sensitivity of the financial market volatility to shocks varies with the volatility level. For this purpose, the paper first introduces the square-root (SQ) GARCH model for financial time series. It is an ARCH analogue of the continuous-time square-root stochastic volatility model popularly used in derivatives pricing and...

We investigate the power and size performance of unit root tests when the true data generating process undergoes Markov regime-switching. All tests, including those robust to a single break in trend growth rate, have very low power against a process with a Markov-switching trend growth rate as in Lam (1990). However, for the case of business cycle non-linearities, unit root tests are very power...

In this paper, we provide a method for modelling stationary time series. We allow the family of marginal densities for the observations to be speci ed. Our approach is to construct the model with a speci ed marginal family and build the dependence structure around it. We show that the resulting time series is linear with a simple autocorrelation structure. In particular, we present an original ...