Improving GARCH volatility forecasts with regime-switching GARCH

Abstract

Many researchers use GARCH models to generate volatility forecasts. Using data on three major U.S. dollar exchange rates we show that such forecasts are too high in volatile periods. We argue that this is due to the high persistence of shocks in GARCH forecasts. To obtain more flexibility regarding volatility persistence, this paper generalizes the GARCH model by distinguishing two regimes with different volatility levels; GARCH effects are allowed within each regime. The resulting Markov regime-switching GARCH model improves on existing variants, for instance by making multi-periodahead volatility forecasting a convenient recursive procedure. The empirical analysis demonstrates that the model resolves the problem with the high single-regime GARCH forecasts and that it yields significantly better outof-sample volatility forecasts.Key words: GARCH, Markov-switching, variance, forecasting, exchange rates. JEL classification: C52, C53, F31. * Department of Economics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, the Netherlands; tel: +31-20-5254191; fax: +31-20-5254254; E-mail: klaassen@fee.uva.nl. I thank Harry Huizinga, Frank de Jong, Michael McAleer, Bertrand Melenberg, Theo Nijman, Arthur van Soest, Kenneth West, the editors of this issue, James Hamilton and Baldev Raj, and two referees for very useful and constructive comments.

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“…The interesting feature of these models lies in the fact that they provide an explanation of the high persistence in volatility, i.e., nearly unit root process for the conditional variance, observed with single-regime GARCH models (Lamoureux and Lastrapes 1990). Furthermore, these models are apt to react quickly to changes in the volatility level (unconditional volatility) which leads to significant improvements in volatility forecasts as shown by Dueker (1997) or Klaassen (2002) for instance. These features make the models attractive for various applications in financial modeling, such as risk management.…”

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“…More details can be found in Klaassen (2002). The advantage of this approach is that it allows to calculate the log likelihood function and multi-step ahead volatility forecasts recursively as in standard GARCH models.…”

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“…Finally, we focused on 2 symmetric distributions, namely the Student-t and Normal distributions. The Student-t distribution has the advantage of being more heavy-tailed than the Normal distribution, making the regimes more stable [25]. Its drawback is that it has one extra parameter (its degree of freedom) which is difficult to estimate [26].…”

“…Regarding maximum likelihood methods, the idea consists in approximating the conditional variance as a sum of past conditional variance expectations as in [26]. This model was later extended by [25] yielding improved volatility forecasts. Alternatively, Haas et al [35] suggested a new formulation for MS-GARCH models by disaggregating the overall variance process into separate processes in each regime.…”

“…For instance, maximum likelihood estimation methods implemented with a numerical optimizer often encounter specific optimization problems due to starting values, inequality constraints or else local minima. Besides, the two formulations of the MS-GARCH model developed in [26] and [25] are based on an approximation for the recursive update of the conditional variance which leads to further estimation complexity. As for the MS-GARCH model in [35], it loses its initial appeal of being analytically tractable along with the inclusion of autoregressive terms in the conditional mean equation which does not match with our model specification to combine AR and GARCH effects with Markov-Switching.…”