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Gaussian Tests of "Extremal White Noise" for Dependent, Heterogeneous, Heavy Tailed Time Series with an Application

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Author Info

  • Jonathan B. Hill

    (Florida International University)

Abstract

We develop asymptotically chi-squared tests of tail specific extremal serial dependence for possibly heavy-tailed time series, including infinite variance and infinite mean processes. Our test statistics have a chi-squared limit distribution under the null of "extremal white-noise" for processes near-epoch-dependent on a mixing process; and obtain a power of one for extremal dependent processes under general conditions. We restrict the NED property to hold only in the extreme support of the distribution, and characterize a broad array of linear and GARCH processes with geometric or hypoberbolic memory that are extremal NED. We apply one-tailed, two-tailed, and difference in tails tests to stock market and exchange rate returns data, and find low levels of significant, persistent, symmetric extremal dependence in the Yen and British Pound, and except for the Shanghai Stock Exchange we find no evidence of extremal dependence in any absolute returns series. A limited study of bivariate volatility spillover in exchange rates reveals extremes in the daily returns of the Yen symmetrically spillover briefly into the Euro after a four day delay, and positive extreme returns in the Euro immediately, and persistently, spillover into the Yen. //

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File URL: http://128.118.178.162/eps/em/papers/0411/0411014.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0411014.

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Length: 54 pages
Date of creation: 18 Nov 2004
Date of revision: 09 Dec 2004
Handle: RePEc:wpa:wuwpem:0411014

Note: Type of Document - pdf; pages: 54
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Web page: http://128.118.178.162

Related research

Keywords: extremal dependence; white-noise; volatility spillover; near-epoch-dependence; regular variation; infinite variance; portmanteau test; exchange rates.;

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References

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  1. Poon, Ser-Huang & Rockinger, Michael & Tawn, Jonathan, 2001. "New Extreme-Value Dependence Measures and Finance Applications," CEPR Discussion Papers 2762, C.E.P.R. Discussion Papers.
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  3. Hentschel, Ludger & Campbell, John, 1992. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," Scholarly Articles 3220232, Harvard University Department of Economics.
  4. Fran├žois Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
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  7. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
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  9. Kokoszka, Piotr S. & Taqqu, Murad S., 1996. "Infinite variance stable moving averages with long memory," Journal of Econometrics, Elsevier, vol. 73(1), pages 79-99, July.
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  11. Carmela Quintos, 2004. "Extremal Correlation for GARCH Data," Econometric Society 2004 North American Summer Meetings 87, Econometric Society.
  12. Runde, Ralf, 1997. "The asymptotic null distribution of the Box-Pierce Q-statistic for random variables with infinite variance an application to German stock returns," Journal of Econometrics, Elsevier, vol. 78(2), pages 205-216, June.
  13. Bekaert, Geert & Harvey, Campbell R., 1997. "Emerging equity market volatility," Journal of Financial Economics, Elsevier, vol. 43(1), pages 29-77, January.
  14. Hong, Yongmiao, 2001. "A test for volatility spillover with application to exchange rates," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 183-224, July.
  15. Liu, Shi-Miin & Brorsen, B Wade, 1995. "Maximum Likelihood Estimation of a Garch-Stable Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 273-85, July-Sept.
  16. Peng, L., 1999. "Estimation of the coefficient of tail dependence in bivariate extremes," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 399-409, July.
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Cited by:
  1. Linton, O. & Whang, Yoon-Jae, 2007. "The quantilogram: With an application to evaluating directional predictability," Journal of Econometrics, Elsevier, vol. 141(1), pages 250-282, November.
  2. Jonathan B. Hill, 2005. "On Tail Index Estimation Using Dependent,Heterogenous Data," Working Papers 0512, Florida International University, Department of Economics.
  3. Jonathan Hill, 2006. "On Functional Central Limit Theorems for Dependent, Heterogeneous Tail Arrays with Applications to Tail Index and Tail Dependence Estimators," Working Papers 0607, Florida International University, Department of Economics.

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