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Small sample properties of GARCH estimates and persistence

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  • Soosung Hwang
  • 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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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal The European Journal of Finance.

Volume (Year): 12 (2006)
Issue (Month): 6-7 ()
Pages: 473-494

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Handle: RePEc:taf:eurjfi:v:12:y:2006:i:6-7:p:473-494

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Keywords: Small sample; volatility; GARCH; persistence;

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References

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Cited by:
  1. 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.
  2. 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, Elsevier, vol. 28(C), pages 1-19.
  3. Peter Hans Matthews, 2004. "Paradise Lost and Found? The Econometric Contributions of Clive W.J. Granger and Robert F. Engle," Middlebury College Working Paper Series 0416, Middlebury College, Department of Economics.
  4. Rodrigo Alfaro & Carmen Gloria Silva, 2008. "Measuring Equity Volatility: the case of Chilean Stock Index," Working Papers Central Bank of Chile, Central Bank of Chile 462, Central Bank of Chile.
  5. 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., Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 45(132), pages 217-233.
  6. David E. Rapach & Jack K. Strauss, 2008. "Structural breaks and GARCH models of exchange rate volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 23(1), pages 65-90.
  7. Michail Karoglou & Panicos Demetriades & Siong Law, 2011. "One date, one break?," Empirical Economics, Springer, Springer, vol. 41(1), pages 7-24, August.
  8. 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.
  9. Essaddam, Naceur & Karagianis, John M., 2014. "Terrorism, country attributes, and the volatility of stock returns," Research in International Business and Finance, Elsevier, Elsevier, vol. 31(C), pages 87-100.
  10. 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.
  11. Umberto Triacca, 2009. "Volatility Persistence and Predictability of Squared Returns in GARCH(1,1) Models," Central European Journal of Economic Modelling and Econometrics, CEJEME, CEJEME, vol. 1(3), pages 285-291, November.
  12. 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.
  13. 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.
  14. Steve Satchell & Soosung Hwang, 2001. "GARCH Model with Cross-sectional Volatility; GARCHX Models," Working Papers, Warwick Business School, Finance Group wp01-16, Warwick Business School, Finance Group.
  15. Jie Zhu, 2009. "Pricing volatility of stock returns with volatile and persistent components," Financial Markets and Portfolio Management, Springer, Springer, vol. 23(3), pages 243-269, September.
  16. 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, Elsevier, vol. 53(6), pages 2168-2188, April.
  17. Geoff Willcocks, 2009. "UK Housing Market: Time Series Processes with Independent and Identically Distributed Residuals," The Journal of Real Estate Finance and Economics, Springer, Springer, vol. 39(4), pages 403-414, November.
  18. 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.
  19. Sen, Chitrakalpa & Chakrabarti, Gagari & Sarkar, Amitava, 1981. "Asymmetric Response in Foreign Exchange Volatility under Structural Break," MPRA Paper 26817, University Library of Munich, Germany.

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