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Small Sample Properties of GARCH Estimates and Persistence

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  • Hwang. S.
  • Pedro L. Valls Pereira

Abstract

It is shown that the ML estimates of the popular GARCH(1,1) model are significantly negatively biased in small samples and that in many cases converged estimates are not possible with Bollerslev's non-negativity conditions. Results also indicate that a high level of persistence in GARCH(1,1) models obtained using a large number of observations has autocorrelations lower than these ML estimates suggest in small samples. Considering the size of biases and convergence errors, it is proposed that at least 250 observations are needed for ARCH(1) models and 500 observations for GARCH(1,1) models. A simple measure of how much GARCH conditional volatility explains squared returns is proposed. The measure indicates that for a typical index return volatility whose ARCH parameter is very small, the conditional volatility hardly explains squared returns.

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Paper provided by Finance Lab, Insper Instituto de Ensino e Pesquisa in its series Finance Lab Working Papers with number flwp_48.

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Date of creation: Oct 2003
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Handle: RePEc:ibm:finlab:flwp_48
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  1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  2. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, School of Economics and Management.
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  7. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  8. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
  9. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
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  12. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
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Cited by:

  1. Essaddam, Naceur & Karagianis, John M., 2014. "Terrorism, country attributes, and the volatility of stock returns," Research in International Business and Finance, Elsevier, vol. 31(C), pages 87-100.
  2. Michail Karoglou & Panicos Demetriades & Siong Law, 2011. "One date, one break?," Empirical Economics, Springer, vol. 41(1), pages 7-24, August.
  3. Soosung Hwang & Steve Satchell, 2005. "GARCH model with cross-sectional volatility: GARCHX models," Applied Financial Economics, Taylor & Francis Journals, vol. 15(3), pages 203-216.
  4. David E. Rapach & Jack K. Strauss, 2008. "Structural breaks and GARCH models of exchange rate volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(1), pages 65-90.
  5. Geoff Willcocks, 2009. "UK Housing Market: Time Series Processes with Independent and Identically Distributed Residuals," The Journal of Real Estate Finance and Economics, Springer, vol. 39(4), pages 403-414, November.
  6. Umberto Triacca, 2009. "Volatility Persistence and Predictability of Squared Returns in GARCH(1,1) Models," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 1(3), pages 285-291, November.
  7. K. Batu Tunay, 2010. "Banking Crises and Early Warning Systems: A Model Suggestion for Turkish Banking Sector," Journal of BRSA Banking and Financial Markets, Banking Regulation and Supervision Agency, vol. 4(1), pages 9-46.
  8. Jie Zhu, 2009. "Pricing volatility of stock returns with volatile and persistent components," Financial Markets and Portfolio Management, Springer, vol. 23(3), pages 243-269, September.
  9. Sen, Chitrakalpa & Chakrabarti, Gagari & Sarkar, Amitava, 1981. "Asymmetric Response in Foreign Exchange Volatility under Structural Break," MPRA Paper 26817, University Library of Munich, Germany.
  10. Rodrigo A. Alfaro & Carmen Gloria Silva, 2008. "Volatilidad de Indices Accionarios: El caso del IPSA," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 45(132), pages 217-233.
  11. Jie Zhu, 2008. "Pricing Volatility of Stock Returns with Volatile and Persistent Components," CREATES Research Papers 2008-14, School of Economics and Management, University of Aarhus.
  12. Hartmann, Matthias & Herwartz, Helmut, 2012. "Causal relations between inflation and inflation uncertainty—Cross sectional evidence in favour of the Friedman–Ball hypothesis," Economics Letters, Elsevier, vol. 115(2), pages 144-147.
  13. Peter Hans Matthews, 2005. "Paradise lost and found? The econometric contributions of Clive W. J. Granger and Robert F. Engle," Review of Political Economy, Taylor & Francis Journals, vol. 17(1), pages 1-28.
  14. Bialkowski, Jedrzej & Gottschalk, Katrin & Wisniewski, Tomasz Piotr, 2008. "Stock market volatility around national elections," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1941-1953, September.
  15. Jie Zhu, 2008. "Testing for Expected Return and Market Price of Risk in Chinese A-B Share Market: A Geometric Brownian Motion and Multivariate GARCH Model Approach," CREATES Research Papers 2008-15, School of Economics and Management, University of Aarhus.
  16. Rodrigo Alfaro & Carmen Gloria Silva, 2008. "Measuring Equity Volatility: the case of Chilean Stock Index," Working Papers Central Bank of Chile 462, Central Bank of Chile.
  17. Fantazzini, Dean, 2009. "The effects of misspecified marginals and copulas on computing the value at risk: A Monte Carlo study," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2168-2188, April.
  18. Jie Zhu, 2008. "FIEGARCH-M and and International Crises: A Cross-Country Analysis," CREATES Research Papers 2008-16, School of Economics and Management, University of Aarhus.
  19. Chau, Frankie & Deesomsak, Rataporn & Wang, Jun, 2014. "Political uncertainty and stock market volatility in the Middle East and North African (MENA) countries," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 28(C), pages 1-19.

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