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Why Frequency Matters for Unit Root Testing

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  • H. Peter Boswijk

    ()
    (Faculty of Economics and Econometrics, Universiteit van Amsterdam)

  • Franc Klaassen

    ()
    (Faculty of Economics and Econometrics, Universiteit van Amsterdam)

Abstract

It is generally believed that for the power of unit root tests, only the time span and not the observation frequency matters. In this paper we show that the observation frequency does matter when the high-frequency data display fat tails and volatility clustering, as is typically the case for financial time series such as exchange rate returns. Our claim builds on recent work on unit root and cointegration testing based non-Gaussian likelihood functions. The essential idea is that such methods will yield power gains in the presence of fat tails and persistent volatility clustering, and the strength of these features (and hence the power gains) increases with the observation frequency. This is illustrated using both Monte Carlo simulations and empirical applications to real exchange rates.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 04-119/4.

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Date of creation: 05 Nov 2005
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Handle: RePEc:dgr:uvatin:20040119

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Web page: http://www.tinbergen.nl

Related research

Keywords: Fat tails; GARCH; mean reversion; observation frequency; purchasing-power parity; unit roots;

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References

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  1. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots," NBER Chapters, in: NBER Macroeconomics Annual 1991, Volume 6, pages 141-220 National Bureau of Economic Research, Inc.
  2. Boswijk, H. Peter & Lucas, Andre, 2002. "Semi-nonparametric cointegration testing," Journal of Econometrics, Elsevier, Elsevier, vol. 108(2), pages 253-280, June.
  3. Klaassen, F.J.G.M., 1999. "Long Swings in Exchange Rates: Are They Really in the Data?," Discussion Paper, Tilburg University, Center for Economic Research 1999-08, Tilburg University, Center for Economic Research.
  4. Drost, F.C. & Nijman, T.E., 1990. "Temporal aggregation of GARCH processes," Discussion Paper, Tilburg University, Center for Economic Research 1990-66, Tilburg University, Center for Economic Research.
  5. Lothian, James R. & Taylor, Mark P., 1997. "Real exchange rate behavior," Journal of International Money and Finance, Elsevier, Elsevier, vol. 16(6), pages 945-954, December.
  6. repec:cup:etheor:v:13:y:1997:i:2:p:149-69 is not listed on IDEAS
  7. H. Peter Boswijk, 2001. "Testing for a Unit Root with Near-Integrated Volatility," Tinbergen Institute Discussion Papers 01-077/4, Tinbergen Institute.
  8. Alan M. Taylor, 2002. "A Century Of Purchasing-Power Parity," The Review of Economics and Statistics, MIT Press, vol. 84(1), pages 139-150, February.
  9. Jeffrey A. Frankel, 1985. "International Capital Mobility and Crowding Out in the U.S. Economy: Imperfect Integration of Financial Markets or of Goods Markets?," NBER Working Papers 1773, National Bureau of Economic Research, Inc.
  10. He, Changli & Teräsvirta, Timo, 1997. "Properties of Moments of a Family of GARCH Processes," Working Paper Series in Economics and Finance 198, Stockholm School of Economics.
  11. H. Peter Boswijk, 2000. "Testing for a Unit Root with Near-Integrated Volatility," Econometric Society World Congress 2000 Contributed Papers 1101, Econometric Society.
  12. Lucas, André, 1997. "Cointegration Testing Using Pseudolikelihood Ratio Tests," Econometric Theory, Cambridge University Press, vol. 13(02), pages 149-169, April.
  13. Shiller, Robert J. & Perron, Pierre, 1985. "Testing the random walk hypothesis : Power versus frequency of observation," Economics Letters, Elsevier, vol. 18(4), pages 381-386.
  14. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, Econometric Society, vol. 49(4), pages 1057-72, June.
  15. Ling, Shiqing & Li, W.K., 2003. "Asymptotic Inference For Unit Root Processes With Garch(1,1) Errors," Econometric Theory, Cambridge University Press, vol. 19(04), pages 541-564, August.
  16. Seo, Byeongseon, 1999. "Distribution theory for unit root tests with conditional heteroskedasticity1," Journal of Econometrics, Elsevier, Elsevier, vol. 91(1), pages 113-144, July.
  17. H. Peter Boswijk & Jurgen A. Doornik, 1999. "Distribution Approximations for Cointegration Tests with Stationary Exogenous Regressors," Tinbergen Institute Discussion Papers 99-013/4, Tinbergen Institute.
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Citations

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Cited by:
  1. Koopman, Siem Jan & Ooms, Marius & Carnero, M. Angeles, 2007. "Periodic Seasonal Reg-ARFIMAGARCH Models for Daily Electricity Spot Prices," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 102, pages 16-27, March.
  2. Ghoshray, Atanu & Johnson, Ben, 2010. "Trends in world energy prices," Energy Economics, Elsevier, Elsevier, vol. 32(5), pages 1147-1156, September.
  3. Charles S. Bos & Siem Jan Koopman & Marius Ooms, 2007. "Long memory modelling of inflation with stochastic variance and structural breaks," CREATES Research Papers 2007-44, School of Economics and Management, University of Aarhus.
  4. Maslyuk, Svetlana & Smyth, Russell, 2008. "Unit root properties of crude oil spot and futures prices," Energy Policy, Elsevier, vol. 36(7), pages 2591-2600, July.

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