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A Bayesian threshold nonlinearity test for financial time series

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

  • Cathy W. S. Chen & Mike K. P. So & Ming-Tien Chen, 2005. "A Bayesian threshold nonlinearity test for financial time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 24(1), pages 61-75.
    • Handle: RePEc:jof:jforec:v:24:y:2005:i:1:p:61-75
    DOI: 10.1002/for.939
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    1. Chen, Cathy W. S. & Chiang, Thomas C. & So, Mike K. P., 2003. "Asymmetrical reaction to US stock-return news: evidence from major stock markets based on a double-threshold model," Journal of Economics and Business, Elsevier, vol. 55(5-6), pages 487-502.
    2. Chen, Cathy W.S. & Gerlach, Richard & So, Mike K.P., 2006. "Comparison of nonnested asymmetric heteroskedastic models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2164-2178, December.
    3. Chen, Cathy W.S. & Gerlach, Richard H. & Tai, Amanda P.J., 2008. "Testing for nonlinearity in mean and volatility for heteroskedastic models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 489-499.
    4. Chen, Cathy W.S. & Chan, Jennifer S.K. & So, Mike K.P. & Lee, Kevin K.M., 2011. "Classification in segmented regression problems," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2276-2287, July.
    5. Caporin, Massimiliano & Gupta, Rangan & Ravazzolo, Francesco, 2021. "Contagion between real estate and financial markets: A Bayesian quantile-on-quantile approach," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    6. Lai, YiHao & Chen, Cathy W.S. & Gerlach, Richard, 2009. "Optimal dynamic hedging via copula-threshold-GARCH models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2609-2624.
    7. Cathy Chen & Feng Liu & Richard Gerlach, 2011. "Bayesian subset selection for threshold autoregressive moving-average models," Computational Statistics, Springer, vol. 26(1), pages 1-30, March.
    8. Jiazhu Pan & Qiang Xia & Jinshan Liu, 2017. "Bayesian analysis of multiple thresholds autoregressive model," Computational Statistics, Springer, vol. 32(1), pages 219-237, March.
    9. Caporin, Massimiliano & Pelizzon, Loriana & Ravazzolo, Francesco & Rigobon, Roberto, 2018. "Measuring sovereign contagion in Europe," Journal of Financial Stability, Elsevier, vol. 34(C), pages 150-181.
    10. Cathy Chen & Simon Lin & Philip Yu, 2012. "Smooth Transition Quantile Capital Asset Pricing Models with Heteroscedasticity," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 19-48, June.
    11. So, Mike K.P. & Chen, Cathy W.S. & Lee, Jen-Yu & Chang, Yi-Ping, 2008. "An empirical evaluation of fat-tailed distributions in modeling financial time series," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(1), pages 96-108.
    12. Nonejad Nima, 2016. "Particle Markov Chain Monte Carlo Techniques of Unobserved Component Time Series Models Using Ox," Journal of Time Series Econometrics, De Gruyter, vol. 8(1), pages 55-90, January.
    13. Varun Agiwal & Jitendra Kumar, 2020. "Bayesian estimation for threshold autoregressive model with multiple structural breaks," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 361-382, December.
    14. Nonejad, Nima, 2014. "Particle Markov Chain Monte Carlo Techniques of Unobserved Component Time Series Models Using Ox," MPRA Paper 55662, University Library of Munich, Germany.
    15. Monica Billio & Roberto Casarin & Francesco Ravazzolo & Herman K. van Dijk, 2011. "Bayesian Combinations of Stock Price Predictions with an Application to the Amsterdam Exchange Index," Tinbergen Institute Discussion Papers 11-082/4, Tinbergen Institute.
    16. Chen, Cathy W.S. & Gerlach, Richard & Wei, D.C.M., 2009. "Bayesian causal effects in quantiles: Accounting for heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1993-2007, April.
    17. Nonejad, Nima, 2017. "Parameter instability, stochastic volatility and estimation based on simulated likelihood: Evidence from the crude oil market," Economic Modelling, Elsevier, vol. 61(C), pages 388-408.
    18. Todd E. Clark & Francesco Ravazzolo, 2012. "The macroeconomic forecasting performance of autoregressive models with alternative specifications of time-varying volatility," Working Papers (Old Series) 1218, Federal Reserve Bank of Cleveland.
    19. Liu, Xiaochun & Luger, Richard, 2015. "Unfolded GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 186-217.

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