Testing multivariate distributions in GARCH models

Journal of Econometrics

Volumn 143, Issue 1, 2008, Pages 19-36

  Bai, Jushan ^a,b   Chen, Zhihong ^c  

^a NEW YORK UNIVERSITY   (United States)

^b Tsinghua University   (China)

^c UNIVERSITY OF INTERNATIONAL BUSINESS AND ECONOMICS   (China)

Author keywords

Brownian motion; Distribution free tests; GARCH; K transformation; Multivariate normality; Multivariate t

Indexed keywords

BROWNIAN MOVEMENT; DISTRIBUTION FUNCTIONS; MULTIVARIABLE CONTROL SYSTEMS; TIME SERIES ANALYSIS;

DISTRIBUTION-FREE TESTS; K-TRANSFORMATION; MULTIVARIATE NORMALITY;

MATHEMATICAL TRANSFORMATIONS;

EID: 38149136597     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jeconom.2007.08.012     Document Type: Article

References (30)

1. Andrews D. A conditional Kolmogorov test. Econometrica 65 (1997) 1097-1128
2. Bai J. Testing parametric conditional distributions of dynamic models. Review of Economics and Statistics 85 (2003) 531-549
3. Bai J., and Ng S. A consistent test for conditional symmetry in time series models. Journal of Econometrics 103 (2001) 225-258
4. Bauwens L., Laurent S., and Rombouts J.V.K. Multivariate GARCH models: a survey. Journal of Applied Econometrics 21 (2006) 79-109
5. Bollerslev T. Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics 31 (1986) 307-327
6. Bollerslev T. A conditionally heteroskedastic time series model for speculative prices and rates of return. Review of Economics and Statistics 69 (1987) 542-547
7. Bowman A.W., and Foster P.J. Adaptive smoothing and density-based tests of multivariate normality. Journal of American Statistical Association 88 (1993) 529-537
8. Delgado, M.A., Stute, W., 2006. Distribution free specification tests of conditional models. Unpublished manuscript.
9. Durbin J. Weak convergence of sample distribution functions when parameters are estimated. Annals of Statistics 1 (1973) 279-290
10. Engle R.F., and Gonzalez-Rivera G. Semiparametric ARCH models. Journal of Business and Economic Statistics 9 (1991) 345-359
11. Epps T., and Pulley L. A test for normality based on the empirical characteristic function. Biometrika 70 (1983) 723-726
12. Erdös P., and Kac M. On certain limit theorems of the theory of probability. Bulletin of the American Mathematical Society 52 (1946) 292-302
13. Henze N., and Zirkler B. A class of invariant consistent tests for multivariate normality. Communications in Statistics-Theory and Methods 19 (1990) 3595-3618
14. Jarque C.M., and Bera A.K. Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Economics Letters 6 (1980) 255-259
15. Jarque C.M., and Bera A.K. A test for normality of observations and regression residuals. International Statistical Review 55 (1987) 163-172
16. Kac M. On deviations between theoretical and empirical distributions. Proceedings of the National Academic Sciences USA 35 (1949) 252-257
17. Khmaladze, E.V., 1981. Martingale approach in the theory of goodness-of-fit tests. In: Theory of Probability and its Applications, vol. XXVI, pp. 240-257.
18. m. The Annals of Statistics 16 (1988) 1503-1516
19. Khmaladze E.V., and Koul H.L. Martingale transforms goodness-of-fit tests in regression models. The Annals of Statistics 32 (2004) 995-1034
20. Kilian L., and Demiroglu U. Residual-based tests for normality in autoregressions: asymptotic theory and simulation evidence. Journal of Business and Economic Statistics 18 (2000) 40-50
21. Kotz S., and Nadarajah S. Multivariate t Distributions and their Applications (2004), Cambridge University Press, New York
22. Koul H.L., and Stute W. Nonparametric model checks for time series. Annals of Statistics 27 (1999) 204-237
23. Luetkepohl H., and Theilen B. Measures of multivariate skewness and kurtosis for tests of nonnormality. Statistical Papers 32 (1991) 179-193
24. Mardia K.V. Measures of multivariate skewness and kurtosis with applications. Biometrika 57 (1970) 519-530
25. Mecklin C.J., and Mundfrom D.J. An appraisal and bibliography of tests for multivariate normality. International Statistical Review 72 (2004) 123-138
26. Richardson M., and Smith T. A test for multivariate normality in stock returns. Journal of Business 66 (1993) 295-321
27. Rosenblatt M. Remarks on a multivariate transformation. Annals of Mathematical Statistics 23 (1952) 470-472
28. Stute W., Thies S., and Zhu L.X. Model checks for regression: an innovation process approach. Annals of Statistics 26 (1998) 1916-1934
29. Tsay R.S. Analysis of Financial Time Series (2002), Wiley, New York
30. Zellner A. An Introduction to Bayesian Inference in Econometrics (1971), Wiley, New York pp. 366-389.