Modeling Multiple Regimes in Financial Volatility With a Flexible Coefficient Garch(1,1) Model

Abstract

In this paper a flexible multiple regime GARCH(1,1)-type model is developed to describe the sign and size asymmetries and intermittent dynamics in financial volatility. The results of the paper are important to other nonlinear GARCH models. The proposed model nests some of the previous specifications found in the literature and has the following advantages. First, contrary to most of the previous models, more than two limiting regimes are possible, and the number of regimes is determined by a simple sequence of tests that circumvents identification problems that are usually found in nonlinear time series models. The second advantage is that the novel stationarity restriction on the parameters is relatively weak, thereby allowing for rich dynamics. It is shown that the model may have explosive regimes but can still be strictly stationary and ergodic. A simulation experiment shows that the proposed model can generate series with high kurtosis and low first-order autocorrelation of the squared observations and exhibit the so-called Taylor effect, even with Gaussian errors. Estimation of the parameters is addressed, and the asymptotic properties of the quasi-maximum likelihood estimator are derived under weak conditions. A Monte-Carlo experiment is designed to evaluate the finite-sample properties of the sequence of tests. Empirical examples are also considered.

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“…As outlined in Hyung et al (2005), a myriad of nonlinear short memory models, especially models with infrequent breaks, can generate data with long memory behavior. Examples of such nonlinear models include the break model of Granger and Hyung (2004), the volatility component model of Engle and Lee (1999), the regime switching model proposed by Hamilton and Susmel (1994), and further discussed in Diebold and Inoue (2001), and the multiple-regime model of Medeiros and Veiga (2004). Hillebrand (2005) also discussed the effects of breaks on the estimation of volatility models (see also Hillebrand and Medeiros, 2006).…”

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