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Modified LR Test

Modified LR Test - Modied Likelihood Ratio Test for Regime...

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Modified Likelihood Ratio Test for Regime Switching Hiroyuki Kasahara Department of Economics University of Western Ontario [email protected] Tatsuyoshi Okimoto Faculty of Economics and IGSSS Yokohama National University [email protected] Katsumi Shimotsu Department of Economics Queen’s University [email protected] March 31, 2008 Abstract This paper proposes a modified quasi-likelihood test of Markov regime switching models. Despite its popularity in economics and finance, there are few papers that develop tests for regime switching models. Recently, Cho and White (2007) derive the asymptotic distribution of the quasi-likelihood ratio (QLR) statistic of Markov regime switching models with a scalar parameter. The asymptotic distribution of the QLR s statistic is, however, a function of a supremum of a Gaussian process that depends on the model structure as well as the parameter space. Further, taking the supremum over the parameter space is often difficult and needs elaborate simulations to obtain precise critical values. We propose a modified quasi-likelihood ratio that substantially simplifies inference of Markov regime switching models. Our approach adds a penalty term to the quasi-likelihood function that controls the inference problem that occurs when the parameter is on the bound- ary. With an appropriate choice of the penalty term, the asymptotic distribution of the modified QLR statistic is a simple function of a standard normal random variable. Conse- quently, the critical values can be easily obtained, and the inference is no more complicated than in the standard case. Our simulation shows that the modified QLR test has good size and power, and its size and power are similar to those of the QLR test. Keywords: Markov regime switching, mixture model, modified likelihood ratio statistic. JEL Classification Numbers: C12, C13, C22. 1
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1 Introduction The Markov regime-switching (RS) model is very attractive to model the dynamics of economic and financial time series, since it can capture many important features, such as structural changes, nonlinearity, high persistence, fat tails, leptokurtosis, and asymmetric dependence. As a consequence, the regime-switching model has been prevalent in economics and finance since Hamilton (1989) proposes it to describe the business cycle. For instance, Evans and Wachtel (1993) use it to analyze the inflation regime and the sources of inflation uncertainty. Hamilton and Susmel (1994) introduce the RS-ARCH model to capture the volatility clustering in stock market more accurately than the GARCH model. Similarly, Gray (1996) develops the RS- GARCH model to examine the conditional distribution of interest rates. The regime-switching framework is also adopted to identify the monetary policy regime as Sims and Zha (2006) and Inoue and Okimoto (2008). In addition, Ang and Bekaert (2001) and Okimoto (2008) employ the regime-switching model to distinguish the bear and bull regimes in international equity markets. Lastly, the regime-switching structure may be critical for evaluating asset price and
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Modified LR Test - Modied Likelihood Ratio Test for Regime...

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