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Asymmetries in conditional mean and variance: modelling stock returns by asMA-asQGARCH

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  • Jan G. De Gooijer

    (University of Amsterdam, The Netherlands)

  • Kurt Brännäs

    (Umeå University, Sweden)

Abstract

We propose a nonlinear time series model where both the conditional mean and the conditional variance are asymmetric functions of past information. The model is particularly useful for analysing financial time series where it has been noted that there is an asymmetric impact of good news and bad news on volatility (risk) transmission. We introduce a coherent framework for testing asymmetries in the conditional mean and the conditional variance, separately or jointly. To this end we derive both a Wald and a Lagrange multiplier test. Some of the new asymmetric model's moment properties are investigated. Detailed empirical results are given for the daily returns of the composite index of the New York Stock Exchange. There is strong evidence of asymmetry in both the conditional mean and the conditional variance functions. In a genuine out-of-sample forecasting experiment the performance of the best fitted asymmetric model, having asymmetries in both conditional mean and conditional variance, is compared with an asymmetric model for the conditional mean, and with no-change forecasts. This is done both in terms of conditional mean forecasting as well as in terms of risk forecasting. Finally, the paper presents some evidence of asymmetries in the index stock returns of the Group of Seven (G7) industrialized countries. Copyright © 2004 John Wiley & Sons, Ltd.

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Bibliographic Info

Article provided by John Wiley & Sons, Ltd. in its journal Journal of Forecasting.

Volume (Year): 23 (2004)
Issue (Month): 3 ()
Pages: 155-171

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Handle: RePEc:jof:jforec:v:23:y:2004:i:3:p:155-171

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Web page: http://www3.interscience.wiley.com/cgi-bin/jhome/2966

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  1. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-53, December.
  2. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  3. repec:att:wimass:9002 is not listed on IDEAS
  4. 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.
  5. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
  6. Sentana,E., 1995. "Quadratic Arch Models," Papers 9517, Centro de Estudios Monetarios Y Financieros-.
  7. Li, C W & Li, W K, 1996. "On a Double-Threshold Autoregressive Heteroscedastic Time Series Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 253-74, May-June.
  8. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
  9. Brannas, K. & Ohlsson, H., 1995. "Asymmetric Cycles and Temporal Aggregation," Papers 1995-11, Uppsala - Working Paper Series.
  10. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  11. Gregory Koutmos, 1999. "Asymmetric index stock returns: evidence from the G-7," Applied Economics Letters, Taylor & Francis Journals, vol. 6(12), pages 817-820.
  12. LeBaron, Blake, 1992. "Some Relations between Volatility and Serial Correlations in Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 65(2), pages 199-219, April.
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Cited by:
  1. Brännäs, Kurt, 2003. "Temporal Aggregation of the Returns of a Stock Index Series," UmeÃ¥ Economic Studies 614, Umeå University, Department of Economics.
  2. Kurt Brannas & Niklas Nordman, 2003. "An alternative conditional asymmetry specification for stock returns," Applied Financial Economics, Taylor & Francis Journals, vol. 13(7), pages 537-541.
  3. Kurt Brannas & Albina Soultanaeva, 2011. "Influence of news from Moscow and New York on returns and risks of Baltic States’ stock markets," Baltic Journal of Economics, Baltic International Centre for Economic Policy Studies, vol. 11(1), pages 109-124, July.
  4. Kulp-Tåg, Sofie, 2007. "Short-Horizon Asymmetric Mean-Reversion and Overreactions: Evidence from the Nordic Stock Markets," Working Papers 524, Hanken School of Economics.
  5. Brännäs Kurt & De Gooijer Jan G. & Lönnbark Carl & Soultanaeva Albina, 2012. "Simultaneity and Asymmetry of Returns and Volatilities: The Emerging Baltic States' Stock Exchanges," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(1), pages 1-24, January.
  6. Taştan, Hüseyin, 2011. "Simulation based estimation of threshold moving average models with contemporaneous shock asymmetry," MPRA Paper 34302, University Library of Munich, Germany.
  7. Malmsten, Hans & Teräsvirta, Timo, 2004. "Stylized Facts of Financial Time Series and Three Popular Models of Volatility," Working Paper Series in Economics and Finance 563, Stockholm School of Economics, revised 03 Sep 2004.
  8. Kurt Brannas & Niklas Nordman, 2003. "Conditional skewness modelling for stock returns," Applied Economics Letters, Taylor & Francis Journals, vol. 10(11), pages 725-728.
  9. Brännäs, Kurt & Soultanaeva, Albina, 2006. "Influence of News in Moscow and New York on Returns and Risks on Baltic State Stock Indices," UmeÃ¥ Economic Studies 696, Umeå University, Department of Economics.

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