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Estimation and Properties of a Time-Varying EGARCH(1,1) in Mean Model

  • Sofia Anyfantaki

    ()

  • Antonis Demos

    ()

    (www.aueb.gr/users/demos)

Time-varying GARCH-M models are commonly employed in econometrics and financial economics. Yet the recursive nature of the conditional variance makes exact likelihood analysis of these models computationally infeasible. This paper outlines the issues and suggests to employ a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a simulated Bayesian solution in only O(T) computational operations, where T is the sample size. Furthermore, the theoretical dynamic properties of a time-varying-parameter EGARCH(1,1)-M are derived. We discuss them and apply the suggested Bayesian estimation to three major stock markets.

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Paper provided by Athens University of Economics and Business in its series DEOS Working Papers with number 1228.

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Date of creation: 30 Jul 2012
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Handle: RePEc:aue:wpaper:1228
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  1. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1997. "Estimation of stochastic volatility models with diagnostics," Journal of Econometrics, Elsevier, vol. 81(1), pages 159-192, November.
  2. Stelios Arvanitis & Antonis Demos, 2004. "Time Dependence and Moments of a Family of Time-Varying Parameter Garch in Mean Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 1-25, 01.
  3. He, Changli & Ter svirta, Timo & Malmsten, Hans, 2002. "Moment Structure Of A Family Of First-Order Exponential Garch Models," Econometric Theory, Cambridge University Press, vol. 18(04), pages 868-885, August.
  4. Sofia Anyfantaki & Antonis Demos, 2012. "Estimation and Properties of a Time-Varying EGARCH(1,1) in Mean Model," DEOS Working Papers 1228, Athens University of Economics and Business.
  5. Vrontos, I D & Dellaportas, P & Politis, D N, 2000. "Full Bayesian Inference for GARCH and EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 187-98, April.
  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. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 361-93, July.
  8. James M. Poterba & Lawrence H. Summers, 1987. "Mean Reversion in Stock Prices: Evidence and Implications," NBER Working Papers 2343, National Bureau of Economic Research, Inc.
  9. Poirier, Dale J., 1998. "Revising Beliefs In Nonidentified Models," Econometric Theory, Cambridge University Press, vol. 14(04), pages 483-509, August.
  10. Chib, Siddhartha, 1993. "Bayes regression with autoregressive errors : A Gibbs sampling approach," Journal of Econometrics, Elsevier, vol. 58(3), pages 275-294, August.
  11. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  12. Antonis Demos, 2002. "Moments and dynamic structure of a time-varying parameter stochastic volatility in mean model," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 345-357, 06.
  13. Sentana, Enrique, 1995. "Quadratic ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 62(4), pages 639-61, October.
  14. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  15. Gabriele Fiorentini & Enrique Sentana Iváñez, 1997. "Identification, estimation and testing of conditionally heteroskedastic factor models," Working Papers. Serie AD 1997-22, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  16. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  17. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
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