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Markov Switching In-Mean Effect. Bayesian Analysis in Stochastic Volatility Framework

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  • Łukasz Kwiatkowski

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    (Cracow University of Economics)

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    Abstract

    In the study we introduce an extension to a stochastic volatility in mean model (SV-M), allowing for discrete regime switches in the risk premium parameter. The logic behind the idea is that neglecting a possibly regimechanging nature of the relation between the current volatility (conditional standard deviation) and asset return within an ordinary SV-M specification may lead to spurious insignificance of the risk premium parameter (as being 'averaged out' over the regimes). Therefore, we allow the volatility in-mean effect to switch over different regimes according to a discrete homogeneous twostate Markov chain. We treat the new specification within the Bayesian framework, which allows to fully account for the uncertainty of model parameters, latent conditional variances and hidden Markov chain state variables. Standard Markov Chain Monte Carlo methods, including the Gibbs sampler and the Metropolis-Hastings algorithm, are adapted to estimate the model and to obtain predictive densities of selected quantities. Presented methodology is applied to analyse series of the Warsaw Stock Exchange index (WIG) and its sectoral subindices. Although rare, once spotted the switching inmean effect substantially enhances the model fit to the data, as measured by the value of the marginal data density.

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    Bibliographic Info

    Article provided by CEJEME in its journal Central European Journal of Economic Modelling and Econometrics.

    Volume (Year): 2 (2010)
    Issue (Month): 1 (January)
    Pages: 59-94

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    Handle: RePEc:psc:journl:v:1:y:2010:i:4:p:59-94

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    Web page: http://cejeme.org/

    Related research

    Keywords: Markov switching; stochastic volatility; risk premium; in-mean effect; Bayesian analysis;

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    1. Pedro L. Valls Pereira, 2004. "How Persistent is Volatility? An Answer with Stochastic Volatility Models with Markov Regime Switching State Equations," Finance Lab Working Papers flwp_59, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    2. Siem Jan Koopman & Eugenie Hol Uspensky, 2002. "The stochastic volatility in mean model: empirical evidence from international stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 667-689.
    3. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
    4. Bauwens, L. & Lubrano, M., . "Bayesian inference on GARCH models using the Gibbs sampler," CORE Discussion Papers RP -1307, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Ray Chou & Robert F. Engle & Alex Kane, 1991. "Measuring Risk Aversion From Excess Returns on a Stock Index," NBER Working Papers 3643, National Bureau of Economic Research, Inc.
    6. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    7. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    8. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
    9. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
    10. So, Mike K P & Lam, K & Li, W K, 1998. "A Stochastic Volatility Model with Markov Switching," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 244-53, April.
    11. Smith, Daniel R, 2002. "Markov-Switching and Stochastic Volatility Diffusion Models of Short-Term Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 183-97, April.
    12. Backus, David K & Gregory, Allan W, 1993. "Theoretical Relations between Risk Premiums and Conditional Variances," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 177-85, April.
    13. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
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