Francq, Christian and Zakoian, JeanMichel (2008): Testing the nullity of GARCH coefficients : correction of the standard tests and relative efficiency comparisons.

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Abstract
This article is concerned by testing the nullity of coefficients in GARCH models. The problem is non standard because the quasimaximum likelihood estimator is subject to positivity constraints. The paper establishes the asymptotic null and local alternative distributions of Wald, score, and quasilikelihood ratio tests. Efficiency comparisons under fixed alternatives are also considered. Two cases of special interest are: (i) tests of the null hypothesis of one coefficient equal to zero and (ii) tests of the null hypothesis of no conditional heteroscedasticity. Finally, the proposed approach is used in the analysis of a set of financial data and leads to reconsider the preeminence of GARCH(1,1) among GARCH models.
Item Type:  MPRA Paper 

Original Title:  Testing the nullity of GARCH coefficients : correction of the standard tests and relative efficiency comparisons 
Language:  English 
Keywords:  Asymptotic efficiency of tests; Boundary; Chibar distribution; GARCH model; Quasi Maximum Likelihood Estimation; Local alternatives 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C2  Single Equation Models; Single Variables > C22  TimeSeries Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  16672 
Depositing User:  Christian Francq 
Date Deposited:  10. Aug 2009 08:03 
Last Modified:  12. Feb 2013 02:46 
References:  Akharif, A. and M. Hallin (2003) Efficient detection of random coefficients in autoregressive models. The Annals of Statistics 31, 675704. Andrews, D. W. K. (2001) Testing when a parameter is on a boundary of the maintained hypothesis. Econometrica 69, 683734. Bahadur, R. R. (1960) Stochastic comparison of tests. The Annals of Mathematical Statistics 31, 276295. Bahadur, R. R. (1967) Rates of convergence of estimates and test statistics. The Annals of Mathematical Statistics 38, 303324. Bartholomew, D. J. (1959) A test of homogeneity of ordered alternatives. Biometrika 46, 3648. Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307327. Bougerol, P. and N. Picard (1992) Stationarity of GARCH processes and of some nonnegative time series. Journal of Econometrics 52, 115127. Carrasco, M. and X. Chen (2002) Mixing and Moment Properties of Various GARCH and Stochastic Volatility Models. Econometric Theory, 18, 1739. Chernoff, H. (1954) On the distribution of the likelihood ratio. Annals of Mathematical Statistics 54, 573578. Demos, A. and E. Sentana (1998) Testing for GARCH effects: A onesided approach. Journal of Econometrics 86, 97127. Drost, F. C. and C. A. J. Klaassen (1997) Efficient estimation in semiparametric GARCH models. Journal of Econometrics 81, 193221. Drost, F. C., Klaassen, C. A. J. and B. J. M. Werker (1997) Adaptive estimation in timeseries models. Annals of Statistics 25, 786817. Dufour, J.M., Khalaf, L., Bernard, J.T. and Genest, I. (2004) Simulationbased finitesample tests for heteroskedasticity and ARCH effects. Journal of Econometrics 122, 317347. Engle, R. F. (1982) Autoregressive conditional heteroskedasticity with estimates of the variance of the United Kingdom inflation. Econometrica 50, 9871007. Francq, C. and JM. Zakoïan (2004) Maximum Likelihood Estimation of Pure GARCH and ARMAGARCH Processes. Bernoulli 10, 605637. Francq, C. and JM. Zakoïan (2006) Mixing properties of a general class of GARCH(1,1) models without moment assumptions on the observed process. Econometric Theory, 22, 815834. Francq, C. and JM. Zakoïan (2007) QuasiMaximum Likelihood Estimation in GARCH Processes when some coefficients are equal to zero. Stochastic Processes and their Applications, 117, 12651284. Gouriéroux, C., Holly A., and A. Monfort (1982) Likelihood Ratio tests, Wald tests, and KuhnTicker Test in Linear Models with inequality constraints on the regression parameters. Econometrica 50, 6380. Hall, P. and Q. Yao (2003) Inference in ARCH and GARCH models with heavytailed errors. Econometrica 71, 285317. Hong, Y. (1997) Onesided ARCH testing in time series models. Journal of Time Series Analysis 18, 253277. Hong, Y. and J. Lee (2001) Onesided testing for ARCH effects using wavelets. Econometric Theory 17, 10511081. King, M. L. and P. X. Wu (1997) Locally optimal onesided tests for multiparameter hypotheses. Econometric Reviews 16, 131156. Klüppelberg, C., Maller R. A., Van de Vyver, M. and D. Wee (2002) Testing for reduction to random walk in autoregressive conditional heteroskedasticity models. The Econometrics Journal 5, 387416. Lee, J. H. H. and M. L. King (1993) A locally most mean powerful based score test for ARCH and GARCH regression disturbances. Journal of Business and Economic Statistics 11, 1727. Ling, S. (2007) Selfweighted LSE and MLE for ARMAGARCH models. Journal of Econometrics 140, 849873. Ling, S. and M. McAleer (2003) Adaptive estimation in nonstationary ARMA models with GARCH noises. Annals of Statistics 31, 642674. Nelson, D. B. and C. Q. Cao (1992) Inequality constraints in the univariate GARCH model. Journal of Business and Economic Statistics 10, 229235. Perlman, M. D. (1969) Onesided testing problems in multivariate analysis. The Annals of mathematical Statistics, 40, 549567. Corrections in The Annals of mathematical Statistics (1971) 42, 1777. Rogers, A. J. (1986) Modified Lagrange multiplyer tests for problems with onesided alternatives. Journal of Econometrics 31, 341361. Shi, N. Z. (1987) Testing a normal mean vector against the alternative determined by a convex cone. Memoirs of the Faculty of Science, Kyushu University, Ser. A 41, 133145. Shi, N. Z. and A. Kudô (1987) The most stringent somewhere most powerful one sided test of the multivariate normal mean. Memoirs of the Faculty of Science, Kyushu University, Ser. A 41, 3744. Silvapulle, M. J. and P. Silvapulle (1995) A score test against onesided alternatives. Journal of the American Statistical Association 90, 342349. van der Vaart, A. W. (1998) Asymptotic statistics. Cambridge University Press, Cambridge. White, H. (1982) Maximum likelihood estimation of misspecified models. Econometrica, 50, 126. Wolak, F. A. (1989) Local and global testing of linear and non linear inequality constraints in non linear econometric models. Econometric Theory 5, 135. Wright, S. P. (1992) Adjusted PValues for Simultaneous Inference S. Paul Wright. Biometrics, 48, 10051013. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/16672 