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One-Sided Testing for ARCH Effect Using Wavelets

  • Jin Lee

    (National University of Singapore)

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    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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    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. 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.
    2. Donald W.K. Andrews, 1994. "Hypothesis Testing with a Restricted Parameter Space," Cowles Foundation Discussion Papers 1060R, Cowles Foundation for Research in Economics, Yale University.
    3. Newey, Whitney K & West, Kenneth D, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Wiley Blackwell, vol. 61(4), pages 631-53, October.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Jensen, Mark J., 2000. "An alternative maximum likelihood estimator of long-memory processes using compactly supported wavelets," Journal of Economic Dynamics and Control, Elsevier, vol. 24(3), pages 361-387, March.
    13. 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.
    14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    15. Demos, Antonis & Sentana, Enrique, 1998. "Testing for GARCH effects: a one-sided approach," Journal of Econometrics, Elsevier, vol. 86(1), pages 97-127, June.
    16. 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.
    17. Maxwell King & Ping Wu, 1997. "Locally optimal one-sided tests for multiparameter hypotheses," Econometric Reviews, Taylor & Francis Journals, vol. 16(2), pages 131-156.
    18. 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.
    19. repec:att:wimass:9520 is not listed on IDEAS
    20. Lee, John H. H., 1991. "A Lagrange multiplier test for GARCH models," Economics Letters, Elsevier, vol. 37(3), pages 265-271, November.
    21. 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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