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Bayesian inference of multiple structural change models with asymmetric GARCH errors

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  • Cathy W. S. Chen

    (Feng Chia University)

  • Bonny Lee

    (Feng Chia University)

Abstract

Structural change in any time series is practically unavoidable, and thus correctly detecting breakpoints plays a pivotal role in statistical modelling. This research considers segmented autoregressive models with exogenous variables and asymmetric GARCH errors, GJR-GARCH and exponential-GARCH specifications, which utilize the leverage phenomenon to demonstrate asymmetry in response to positive and negative shocks. The proposed models incorporate skew Student-t distribution and prove the advantages of the fat-tailed skew Student-t distribution versus other distributions when structural changes appear in financial time series. We employ Bayesian Markov Chain Monte Carlo methods in order to make inferences about the locations of structural change points and model parameters and utilize deviance information criterion to determine the optimal number of breakpoints via a sequential approach. Our models can accurately detect the number and locations of structural change points in simulation studies. For real data analysis, we examine the impacts of daily gold returns and VIX on S&P 500 returns during 2007–2019. The proposed methods are able to integrate structural changes through the model parameters and to capture the variability of a financial market more efficiently.

Suggested Citation

  • Cathy W. S. Chen & Bonny Lee, 2021. "Bayesian inference of multiple structural change models with asymmetric GARCH errors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 1053-1078, September.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:3:d:10.1007_s10260-020-00549-z
    DOI: 10.1007/s10260-020-00549-z
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    1. Zeileis, Achim & Kleiber, Christian & Kramer, Walter & Hornik, Kurt, 2003. "Testing and dating of structural changes in practice," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 109-123, October.
    2. Inclan, Carla, 1993. "Detection of Multiple Changes of Variance Using Posterior Odds," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 289-300, July.
    3. M. Hashem Pesaran & Davide Pettenuzzo & Allan Timmermann, 2006. "Forecasting Time Series Subject to Multiple Structural Breaks," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 1057-1084.
    4. Davis, Richard A. & Lee, Thomas C.M. & Rodriguez-Yam, Gabriel A., 2006. "Structural Break Estimation for Nonstationary Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 223-239, March.
    5. 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.
    6. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    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. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Pesaran, M. Hashem & Timmermann, Allan, 2004. "How costly is it to ignore breaks when forecasting the direction of a time series?," International Journal of Forecasting, Elsevier, vol. 20(3), pages 411-425.
    10. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    11. Dima Alberg & Haim Shalit & Rami Yosef, 2008. "Estimating stock market volatility using asymmetric GARCH models," Applied Financial Economics, Taylor & Francis Journals, vol. 18(15), pages 1201-1208.
    12. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    13. Thomas C. Chiang & Cathy W.S. Chen & Mike K.P. So, 2007. "Asymmetric Return and Volatility Responses to Composite News from Stock Markets," Multinational Finance Journal, Multinational Finance Journal, vol. 11(3-4), pages 179-210, September.
    14. Bonnie K. Ray & Ruey S. Tsay, 2002. "Bayesian methods for change‐point detection in long‐range dependent processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(6), pages 687-705, November.
    15. Kim, Chang-Jin & Nelson, Charles R & Piger, Jeremy, 2004. "The Less-Volatile U.S. Economy: A Bayesian Investigation of Timing, Breadth, and Potential Explanations," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 80-93, January.
    16. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
    17. Manh Cuong Dong & Cathy W. S. Chen & Sangyoel Lee & Songsak Sriboonchitta, 2019. "How Strong is the Relationship Among Gold and USD Exchange Rates? Analytics Based on Structural Change Models," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 343-366, January.
    18. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
    19. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    20. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    21. 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.
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