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Periodic Stochastic Volatility and Fat Tails

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  • Ilias Tsiakas

Abstract

This article provides a comprehensive analysis of the size and statistical significance of the day of the week, month of the year, and holiday effects in daily stock index returns and volatility. We employ data from the Dow Jones Industrial Average (DJIA), the S&P 500, the S&P MidCap 400, and the S&P SmallCap 600 in order to test whether the seasonal patterns of medium and small firms are similar to those of large firms. Using formal hypothesis tests based on bootstrapping, we demonstrate that there are more significant calendar effects in volatility than in expected returns, especially for the two large cap indices. More importantly, we introduce the periodic stochastic volatility (PSV) model for characterizing the observed seasonal patterns of daily financial market volatility. We analyze the interaction between seasonal heteroskedasticity and fat tails by comparing the performance of Gaussian PSV and fat-tailed PSVt specifications to the plain vanilla SV and SVt benchmarks. Consistent with our model-free results, we find strong evidence of seasonal periodicity in volatility, which essentially eliminates the need for a fat-tailed conditional distribution, and is robust to the exclusion of the crash of 1987 outliers. Copyright 2006, Oxford University Press.
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  • Ilias Tsiakas, 2004. "Periodic Stochastic Volatility and Fat Tails," Working Papers wp04-09, Warwick Business School, Finance Group.
  • Handle: RePEc:wbs:wpaper:wp04-09
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    References listed on IDEAS

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    1. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
    2. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
    3. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    4. Andersen, Torben G. & Bollerslev, Tim & Lange, Steve, 1999. "Forecasting financial market volatility: Sample frequency vis-a-vis forecast horizon," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 457-477, December.
    5. Maureen O'Hara, 2003. "Presidential Address: Liquidity and Price Discovery," Journal of Finance, American Finance Association, vol. 58(4), pages 1335-1354, August.
    6. Hasbrouck, Joel & Seppi, Duane J., 2001. "Common factors in prices, order flows, and liquidity," Journal of Financial Economics, Elsevier, vol. 59(3), pages 383-411, March.
    7. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    8. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
    9. Hasbrouck, Joel, 1993. "Assessing the Quality of a Security Market: A New Approach to Transaction-Cost Measurement," Review of Financial Studies, Society for Financial Studies, vol. 6(1), pages 191-212.
    10. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2004. "Analytical Evaluation Of Volatility Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1079-1110, November.
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    Cited by:

    1. Eduardo Rossi & Dean Fantazzini, 2015. "Long Memory and Periodicity in Intraday Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 13(4), pages 922-961.
    2. Hüseyin Kaya & Sadullah Çelik, 2009. "Empirical Evidence For Day Of The Week Effect In An Emerging Market: The Turkish Case," 2009 Meeting Papers 219, Society for Economic Dynamics.
    3. Qadan, Mahmoud & Kliger, Doron, 2016. "The short trading day anomaly," Journal of Empirical Finance, Elsevier, vol. 38(PA), pages 62-80.
    4. repec:spr:sistpr:v:20:y:2017:i:2:d:10.1007_s11203-016-9139-z is not listed on IDEAS
    5. Tsiakas, Ilias, 2008. "Overnight information and stochastic volatility: A study of European and US stock exchanges," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 251-268, February.
    6. Yermack, David, 2014. "Tailspotting: Identifying and profiting from CEO vacation trips," Journal of Financial Economics, Elsevier, vol. 113(2), pages 252-269.
    7. Imtiaz Mazumder, M. & Chu, Ting-Heng & Miller, Edward M. & Prather, Larry J., 2008. "International day-of-the-week effects: An empirical examination of iShares," International Review of Financial Analysis, Elsevier, vol. 17(4), pages 699-715, September.
    8. M. Imtiaz Mazumder & Edward M. Miller & Oscar A. Varela, 2010. "Market Timing the Trading of International Mutual Funds: Weekend, Weekday and Serial Correlation Strategies," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 37(7-8), pages 979-1007.
    9. Charles, Amélie, 2010. "The day-of-the-week effects on the volatility: The role of the asymmetry," European Journal of Operational Research, Elsevier, vol. 202(1), pages 143-152, April.
    10. Ilias Tsiakas, 2010. "The Economic Gains Of Trading Stocks Around Holidays," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 33(1), pages 1-26.
    11. Giovanis, Eleftherios, 2009. "Calendar Effects and Seasonality on Returns and Volatility," MPRA Paper 64404, University Library of Munich, Germany.
    12. Fernando F. Ferreira & A. Christian Silva & Ju-Yi Yen, 2014. "Information ratio analysis of momentum strategies," Papers 1402.3030, arXiv.org, revised Jul 2014.
    13. Bidarkota, Prasad V. & Dupoyet, Brice V. & McCulloch, J. Huston, 2009. "Asset pricing with incomplete information and fat tails," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1314-1331, June.
    14. Aknouche, Abdelhakim, 2013. "Periodic autoregressive stochastic volatility," MPRA Paper 69571, University Library of Munich, Germany, revised 2015.
    15. Ilias Tsiakas, 2004. "Analysis of the predictive ability of information accumulated over nights, weekends and holidays," Econometric Society 2004 Australasian Meetings 208, Econometric Society.
    16. Aknouche, Abdelhakim & Al-Eid, Eid & Demouche, Nacer, 2016. "Generalized quasi-maximum likelihood inference for periodic conditionally heteroskedastic models," MPRA Paper 75770, University Library of Munich, Germany, revised 19 Dec 2016.
    17. David Yermack, 2012. "Tailspotting: Identifying and profiting from CEO vacation trips," NBER Working Papers 17940, National Bureau of Economic Research, Inc.

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