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One-Sided Testing for ARCH Effect Using Wavelets

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  • Jin Lee

    (National University of Singapore)

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    Abstract

    There has been an increasing interest in hypothesis testing with inequality restrictions. An important example in time series econometrics is hypotheses on autoregressive conditional heteroskedasticity (ARCH). We propose a one-sided test for ARCH using the wavelet method, a new analytic tool developed in the last decade or so. The test is based on a wavelet spectral density estimator at frequency zero of the square of estimated residuals from a regression model. The square of an ARCH\ process is positively correlated at all lags, resulting in a spectral mode at frequency zero. In particular, it has a spectral peak at frequency zero when there exists persistent ARCH, or when ARCH effect is small at each lag but carries over a long distributional lag. Because wavelets can effectively capture spectral peaks, we expect that the wavelet test is more powerful than the kernel counterpart when there exists persistent ARCH or when ARCH effect has a long distributional lag. This is confirmed in a simulation study, which also compares a number of important one-sided and two-sided ARCH tests.

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    Bibliographic Info

    Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1214.

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    Date of creation: 01 Aug 2000
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    Handle: RePEc:ecm:wc2000:1214

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    1. Bera, A.K. & Higgins, M.L., 1990. "A Test For Conditional Heterskedasticity In Time Series Midels," University of Western Ontario, The Centre for the Study of International Economic Relations Working Papers 9003, University of Western Ontario, The Centre for the Study of International Economic Relations.
    2. Lee, John H H & King, Maxwell L, 1994. "Correction [A Locally Most Mean Powerful Based Score Test for ARCH and GARCH Regression Disturbances]," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 139, January.
    3. repec:att:wimass:9220 is not listed on IDEAS
    4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    5. repec:att:wimass:9520 is not listed on IDEAS
    6. Andrews, Donald W. K., 1998. "Hypothesis testing with a restricted parameter space," Journal of Econometrics, Elsevier, vol. 84(1), pages 155-199, May.
    7. Mark J. Jensen, 1997. "An Alternative Maximum Likelihood Estimator of Long-Memeory Processes Using Compactly Supported Wavelets," Econometrics 9709002, EconWPA.
    8. Donald W.K. Andrews, 1999. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Cowles Foundation Discussion Papers 1229, Cowles Foundation for Research in Economics, Yale University.
    9. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
    10. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
    11. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    12. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
    13. Wu, P.X. & King, M.L., 1994. "One Sided Hypothesis Testing in Econometrics: A Survey," Monash Econometrics and Business Statistics Working Papers 6/94, Monash University, Department of Econometrics and Business Statistics.
    14. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
    15. Maxwell King & Ping Wu, 1997. "Locally optimal one-sided tests for multiparameter hypotheses," Econometric Reviews, Taylor & Francis Journals, vol. 16(2), pages 131-156.
    16. Lee, John H. H., 1991. "A Lagrange multiplier test for GARCH models," Economics Letters, Elsevier, vol. 37(3), pages 265-271, November.
    17. Kenneth D. West & Whitney K. Newey, 1995. "Automatic Lag Selection in Covariance Matrix Estimation," NBER Technical Working Papers 0144, National Bureau of Economic Research, Inc.
    18. Demos, Antonis & Sentana, Enrique, 1998. "Testing for GARCH effects: a one-sided approach," Journal of Econometrics, Elsevier, vol. 86(1), pages 97-127, June.
    19. Lee, John H H & King, Maxwell L, 1993. "A Locally Most Mean Powerful Based Score Test for ARCH and GARCH Regression Disturbances," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 17-27, January.
    20. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    21. Robert F. Engle & David F. Hendry & David Trumble, 1985. "Small-Sample Properties of ARCH Estimators and Tests," Canadian Journal of Economics, Canadian Economics Association, vol. 18(1), pages 66-93, February.
    22. Wolak, Frank A., 1989. "Testing inequality constraints in linear econometric models," Journal of Econometrics, Elsevier, vol. 41(2), pages 205-235, June.
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