# Modeling Financial Time Series Volatility with Markov Switching Models

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## Abstract

Microsoft Word - 19_Kosko_Pietrzak.docx © Co py rig ht b y T he N ico lau s C op er nic us U niv er sit y S cie nt ifi c P ub lis hin g H ou se DYNAMIC ECONOMETRIC MODELS Vol. 8 – Nicolaus Copernicus University – Toruń – 2008 Monika Kośko The University of Computer Science and Economics in Olsztyn Michał Pietrzak∗ Nicolaus Copernicus University Modeling Financial Time Series Volatility with Markov Switching Models 1. Introduction An analysis of financial time series volatility is an important issue in mak- ing many economic decisions. The volatility of high frequency financial series changes over time and the periods of the high volatility are clustering. Many au- thors use GARCH models, introduced by Bollerslev (1986), to capture these dependences. GARCH models describe the conditional variance clustering ef- fect but their forecasts are often overstated (Anderson and Bollerslev, 1998). An application of the Markov switching specification to GARCH models can out- perform forecasts of the standard GARCH structure. The first Markov switching model was used by Hamilton (1989) in the analysis of the business cycle. The ARCH model with Markov switching (SWARCH) was the first specification in this class of models (Hamilton, Susmel, 1994). Next the SWARCH structure was extended to GARCH parameters, giving the MS-GARCH model. The Mar- kov switching GARCH model was characterized by Davidson (1994), Klassen (2002) and Gray (1996), and each of them defined an equation of the condition- al variance in a different way. The conditional variance equation is then ex- ploited in the estimation of MS-GARCH model parameters. The main purpose of this article is to check whether, a better quality volatili- ty predictions can be obtained from MS-AR-GARCH than from AR-GARCH models. At first the estimation of those types of models has been carried out for ∗ In the case of Michał Pietrzak the pub

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