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A Bayesian threshold nonlinearity test for financial time series

  • Cathy W. S. Chen

    (Feng Chia University, Taiwan)

  • Mike K. P. So

    (Hong Kong University of Science and Technology, Hong Kong)

  • Ming-Tien Chen

    (Feng Chia University, Taiwan)

We propose in this paper a threshold nonlinearity test for financial time series. Our approach adopts reversible-jump Markov chain Monte Carlo methods to calculate the posterior probabilities of two competitive models, namely GARCH and threshold GARCH models. Posterior evidence favouring the threshold GARCH model indicates threshold nonlinearity or volatility asymmetry. Simulation experiments demonstrate that our method works very well in distinguishing GARCH and threshold GARCH models. Sensitivity analysis shows that our method is robust to misspecification in error distribution. In the application to 10 market indexes, clear evidence of threshold nonlinearity is discovered and thus supporting volatility asymmetry. Copyright © 2005 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/for.939
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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Forecasting.

Volume (Year): 24 (2005)
Issue (Month): 1 ()
Pages: 61-75

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Handle: RePEc:jof:jforec:v:24:y:2005:i:1:p:61-75
DOI: 10.1002/for.939
Contact details of provider: Web page: http://www3.interscience.wiley.com/cgi-bin/jhome/2966

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  1. So, Mike K P & Li, W K & Lam, K, 2002. "A Threshold Stochastic Volatility Model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 21(7), pages 473-500, November.
  2. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
  3. Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
  4. 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.
  5. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
  6. 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.
  7. Christie, Andrew A., 1982. "The stochastic behavior of common stock variances : Value, leverage and interest rate effects," Journal of Financial Economics, Elsevier, vol. 10(4), pages 407-432, December.
  8. Gourieroux, Christian & Monfort, Alain, 1992. "Qualitative threshold ARCH models," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 159-199.
  9. Brooks, Chris, 2001. "A Double-Threshold GARCH Model for the French Franc/Deutschmark Exchange Rate," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(2), pages 135-43, March.
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