Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2010 | 2 | nr 1 | 59--94
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
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 regime- changing 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 two-state 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 in-mean effect substantially enhances the model fit to the data, as measured by the value of the marginal data density. (original abstract)
Opis fizyczny
  • Cracow University of Economics, Poland
  • [1] Backus D.K., Gregory A.W., (1993), Theoretical Relations Between Risk Premiums and Conditional Variances, Journal of Business & Economic Statistics 11 (no. 2), 177-185.
  • [2] Bauwens L., Lubrano M., (1998), Bayesian inference on GARCH models using the Gibbs sampler, Econometrics Journal 1, C23-C46.
  • [3] Carter C.K., Kohn R., (1994), On Gibbs sampling for state space models, Biometrika 81, 541-553.
  • [4] Carvalho C.M., Lopes H.F., (2006), Simulation-based sequential analysis of Markov switching stochastic volatility models, Computational Statistics & Data Analysis, doi: 10.1016/j.csda.2006.07.019
  • [5] Casarin R., (2003), Bayesian Inference for Generalised Markov Switching Stochastic Volatility Models, Conference materials at the 4th International Workshop on Objective Bayesian Methodology, CNRS, Aussois.
  • [6] Chib S., (1996), Calculating posterior distributions and modal estimates in Markov mixture models, Journal of Econometrics 75, 79-97.
  • [7] Chou R., Engle R.F., Kane A., (1992), Measuring Risk Aversion from Excess Returns on a Stock Index, Journal of Econometrics 52, 201-224.
  • [8] Engle R.F., (1982), Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom In ation, Econometrica 50, 987-1007.
  • [9] Engle R.F., Lilien D.M., Robins R.P., (1987), Estimating time varying risk premia in the term structure: The ARCH-M model, Econometrica 55, 525-542.
  • [10] Fiszeder P., Kwiatkowski J., (2005a), Model GARCH-M ze zmiennym parametrem - analiza wybranych spółek i indeksów notowanych na GPW w Warszawie (GARCH-M Model with Time-Varying Parameter - Analysis of Selected Stock and Indices Quoted on the WSE, in Polish), Statistical Review (Przegląd Statystyczny) 52 (no. 3), 73-88.
  • [11] Fiszeder P., Kwiatkowski J., (2005b), Dynamic Analysis of Relation between Expected Return and Conditional Variance, Acta Universitatis Nicolai Copernici 372, 85-98.
  • [12] Gärtner D., (2007), Why Bayes Rules: A Note on Bayesian vs. Classical Inference in Regime Switching Models, Working Paper No. 0719, Socioeconomic Institute, University of Zürich.
  • [13] Glosten L.R., Jagannathan R., Runkle D.E., (1993), On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks, Journal of Finance 48, 1791-1801.
  • [14] Hamilton J. D., (1989), A New approach to the economic analysis of nonstationary time series and the business cycle, Econometrica 57, 357-384.
  • [15] Hwang S., Satchell S.E., Pereira P.L.V., (2004), Stochastic Volatility Models with Markov Regime Switching State Equations, Journal of Business and Economic Statistics 16
  • [16] Jacquier E., Polson N., Rossi P., (1994), Bayesian analysis of stochastic volatility models (with discussion), Journal of Business and Economic Statistics 12, 371- 417.
  • [17] Kalimipalli M., Susmel R., (2001), Regime-switching stochastic volatility and short-term interest rates, CEMA Working Papers, available at:
  • [18] Koopman S.J., Hol Uspensky E., (2002), The Stochastic Volatility In Mean Model: Empirical Evidence from International Stock Markets, Journal of Applied Econometrics 17, 667-689.
  • [19] Kwiatkowski Ł., (2009a), Markov switching SV processes in modelling volatility of financial time series, Statistical Review (Przegląd Statystyczny), 56 (1), 147-168.
  • [20] Kwiatkowski Ł., (2009b), Markov switching in stochastic variance. Bayesian comparison of two simple models, Folia Oeconomica Cracoviensia 49-50, 107-141.
  • [21] N'dri K.L., (2008), An Empirical Study of the Relation between Stock Market Returns and Volatility in the BRVM, International Research Journal of Finance and Economics 14, 8-14.
  • [22] Nelson D.B., (1991), Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica 59, 347-370.
  • [23] Newton M.A., Raftery A.E., (1994), Approximate Bayesian inference by Weighted Likelihood Bootstrap (with discussion), Journal of the Royal Statistical Society, series B 56, 3-48.
  • [24] Osiewalski J., Pipień M., (2000), GARCH-In-Mean through skewed t conditional distributions: Bayesian inference for exchange rates, [in:] 26-th International Conference MACROMODELS'99, [ed:] W. Welfe, P. Wdowi«ski, Łódź, 354-369.
  • [25] Pajor A., (2003), Procesy zmienności stochastycznej SV w bayesowskiej analizie finansowych szeregów czasowych (Stochastic Volatility Processes in Bayesian Analysis of Financial Time Series, in Polish), Cracow University of Economics.
  • [26] Pipień M., (2007), An approach to measuring the relation between risk and return. Bayesian analysis for WIG data, Folia Oeconomica Cracoviensia 48, 95-117.
  • [27] Pipień M., Osiewalski J., (2001), Model GARCH-M(1,1): specyfikacja i estymacja bayesowska (A GARCH-M(1,1) Model: Specification and Bayesian Estimation, in Polish), Prace Naukowe Akademii Ekonomicznej we Wrocławiu (no. 895), 188-197.
  • [28] Scruggs J.T., (1998), Resolving the Puzzling Intertemporal Relation between the Market Risk Premium and Conditional Market Variance: A Two-Factor Approach, Journal of Finance 53, 575-603.
  • [29] Shibata M., Watanabe T., (2005), Bayesian analysis of a Markov switching stochastic volatility model, Journal of Japan Statistical Society 35, 205-219.
  • [30] Smith D. R., (2002), Markov-Switching and Stochastic Volatility Diffusion Models for Short-Term Interest Rates, Journal of Business and Economic Statistics 20, 183-197.
  • [31] So M. K. P., Lam K., Li W. K., (1998), A stochastic volatility model with Markov switching, Journal of Business and Economic Statistics 16, 244-253.
  • [32] Valls Pereira P.L., (2004), How Persistent is Volatility? An Answer with Stochastic Volatility Models with Markov Regime Switching State Equations, Finance Lab Working Papers wp_59, Finance Lab, Ibmec Sao Paulo.
Typ dokumentu
Identyfikator YADDA

Zgłoszenie zostało wysłane

Zgłoszenie zostało wysłane

Musisz być zalogowany aby pisać komentarze.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.