The use of Markov-switching models to capture the volatility dynamics of financial time series has grown considerably during past years, in part because they give rise to a plausible interpretation of nonlinearities. Nevertheless, GARCH-type models remain ubiquitous in order to allow for nonlinearities associated with time-varying volatility. Existing methods of combining the two approaches are unsatisfactory, as they either suffer from severe estimation difficulties or else their dynamic properties are not well understood. In this article we present a new Markov-switching GARCH model that overcomes both of these problems. Dynamic properties are derived and their implications for the volatility process discussed. We argue that the disaggregation of the variance process offered by the new model is more plausible than in the existing variants. The approach is illustrated with several exchange rate return series. The results suggest that a promising volatility model is an independent switching GARCH process with a possibly skewed conditional mixture density.

In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. The construction of “observable” or realized volatility series from intra-day transaction data and the use of standard time-series techniques has lead to promising strategies for modeling and predicting (daily) volatility. In this article, we show that the residuals of commonly used time-series models for realized volatility and logarithmic realized variance exhibit non-Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance for modeling and forecasting realized volatility. In an empirical application for S&P 500 index futures we show that allowing for time-varying volatility of realized volatility and logarithmic realized variance substantially improves the fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting.

Both unconditional mixed normal distributions and GARCH models with fat-tailed conditional distributions have been employed in the literature for modeling financial data. We consider a mixed normal distribution coupled with a GARCH-type structure (termed MN-GARCH) which allows for conditional variance in each of the components as well as dynamic feedback between the components. Special cases and relationships with previously proposed specifications are discussed and stationarity conditions are derived. For the empirically most relevant GARCH(1,1) case, the conditions for existence of arbitrary integer moments are given and analytic expressions of the unconditional skewness, kurtosis, and autocorrelations of the squared process are derived. Finally, employing daily return data on the NASDAQ index, we provide a detailed empirical analysis and compare both the in-sample fit and out-of-sample forecasting performance of the MN-GARCH as well as recently proposed Markov-switching models. We show that the MN-GARCH approach can generate a plausible disaggregation of the conditional variance process in which the components' volatility dynamics have a clearly distinct behavior, which is, for example, compatible with the well-known leverage effect.