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A Locally Most Mean Powerful Based Score Test for ARCH and GARCH Regression Disturbances

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  • Lee, John H H
  • King, Maxwell L

Abstract

This paper considers testing for autoregressive conditional heteroskedasticity and generalized autoregressive conditional heteroskedasticity disturbances in the linear regression model. These testing problems are one-sided in nature; a fact ignored by the Lagrange multiplier test. A test that exploits this one-sided aspect is constructed based on the sum of the scores. The size and power properties of two versions of this test under normal and leptokurtic disturbances are investigated via a Monte Carlo experiment. The results indicate that both version s of the new test typically have superior power to two versions of the Lagrange multiplier test and possibly also more accurate asymptotic critical values.

Suggested Citation

  • 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.
  • Handle: RePEc:bes:jnlbes:v:11:y:1993:i:1:p:17-27
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    Cited by:

    1. Dufour, Jean-Marie & Khalaf, Lynda & Bernard, Jean-Thomas & Genest, Ian, 2004. "Simulation-based finite-sample tests for heteroskedasticity and ARCH effects," Journal of Econometrics, Elsevier, vol. 122(2), pages 317-347, October.
    2. Marie-Claude BEAULIEU & Jean-Marie DUFOUR & Lynda KHALAF, 2002. "Testing Mean-Variance Efficiency In Capm With Possibly Non-Gaussian Errors : An Exact Simulation-Based Approach," Cahiers de recherche 17-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
    4. Shaun Bond & Stephen Satchell, 2006. "Asymmetry and downside risk in foreign exchange markets," The European Journal of Finance, Taylor & Francis Journals, vol. 12(4), pages 313-332.
    5. Catani, P.S. & Ahlgren, N.J.C., 2017. "Combined Lagrange multiplier test for ARCH in vector autoregressive models," Econometrics and Statistics, Elsevier, vol. 1(C), pages 62-84.
    6. Rahman, Shahidur & King, Maxwell L., 1997. "Marginal-likelihood score-based tests of regression disturbances in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 82(1), pages 81-106.
    7. Lundbergh, Stefan & Terasvirta, Timo, 2002. "Evaluating GARCH models," Journal of Econometrics, Elsevier, vol. 110(2), pages 417-435, October.
    8. Mckenzie, Michael D., 1998. "The impact of exchange rate volatility on Australian trade flows," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 8(1), pages 21-38, January.
    9. Oliver Linton & Douglas Steigerwald, 2000. "Adaptive testing in arch models," Econometric Reviews, Taylor & Francis Journals, vol. 19(2), pages 145-174.
    10. van Dijk, Dick & Franses, Philip Hans & Lucas, Andre, 1999. "Testing for ARCH in the Presence of Additive Outliers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 539-562, Sept.-Oct.
    11. Francis X. Diebold & Jose A. Lopez, 1995. "Measuring Volatility Dynamics," NBER Technical Working Papers 0173, National Bureau of Economic Research, Inc.
    12. Beaulieu, Marie-Claude & Dufour, Jean-Marie & Khalaf, Lynda, 2010. "Asset-pricing anomalies and spanning: Multivariate and multifactor tests with heavy-tailed distributions," Journal of Empirical Finance, Elsevier, vol. 17(4), pages 763-782, September.
    13. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
    14. Demos, Antonis & Sentana, Enrique, 1998. "Testing for GARCH effects: a one-sided approach," Journal of Econometrics, Elsevier, vol. 86(1), pages 97-127, June.
    15. Brooks, Robert D. & Davidson, Sinclair & Faff, Robert W., 1997. "An examination of the effects of major political change on stock market volatility: the South African experience," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 7(3), pages 255-275, October.
    16. McKenzie, Michael D. & Brooks, Robert D., 1997. "The impact of exchange rate volatility on German-US trade flows," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 7(1), pages 73-87, April.
    17. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    18. Christian Francq & Jean-Michel Zakoïan, 2006. "Inference in GARCH when some coefficients are equal to zero," Computing in Economics and Finance 2006 64, Society for Computational Economics.
    19. Duchesne, Pierre, 2004. "On robust testing for conditional heteroscedasticity in time series models," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 227-256, June.
    20. Hughes, Anthony W. & King, Maxwell L. & Kwek, Kian Teng, 2004. "Selecting the order of an ARCH model," Economics Letters, Elsevier, vol. 83(2), pages 269-275, May.
    21. Jin Lee, 2000. "One-Sided Testing for ARCH Effect Using Wavelets," Econometric Society World Congress 2000 Contributed Papers 1214, Econometric Society.

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