Testing Constraints and Misspecification in VAR-ARCH Models
Vector autoregressive models with conditional heteroskedastic errors (abbreviated as VAR-ARCH models) have become increasingly important for applications in financial econometrics. In this paper, we propose likelihood ratio and Wald tests for constraints and the White (1982) misspecification test for VAR-ARCH models which are estimated by the maximum likelihood (ML) method. The tests are discussed for a general class of multivariate conditional heteroskedastic time series models including the VAR-ARCH models. We derive the exact analytic expression for the gradient vector and the conditional information matrix from the log-likelihood function under the normality assumption.
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- BERNDT, E., HALL, B., HALL, R. and HAUSMAN, J. (1974): Estimation and inference in nonlinear structural models. Annals of Economic and Social Measurement, 3, 653–665.Google Scholar
- LIU, S. and POLASEK, W. (1999): Maximum likelihood estimation for the VAR-VARCH model: A new approach. In: U. Leopold-Wildburger, G. Feichtinger, and K.-P. Kistner (Eds.): Modelling and Decisions in Economics, Essays in Honor of Franz Ferschl. Physica-Verlag, Heidelberg, 99–113.Google Scholar
- MAGNUS, J.R. and NEUDECKER, H. (1999): Matrix Differential Calculus with Applications in Statistics and Econometrics, revised edition. John Wiley and Sons, Chichester, UK.Google Scholar
- MATHSOFT (1996): S+GARCH User’s Manual, Version 1.0. Data Analysis Products Division, MathSoft, Seattle, USA.Google Scholar
- MILLS, T.C. (1994): The Econometric Modelling of Financial Time Series. Cambridge University Press, Cambridge, UK.Google Scholar
- POLASEK, W. (1999): The BASEL package: A Bayesian Sampling Environment Language. University of Basel, Basel, Switzerland.Google Scholar
- WHITE, H. (1988): White tests of misspecification. In: S. Kotz, N.L. Johnson and C.B. Read, ed. Encyclopedia of Statistical sciences, vol. 9, 594–596, John Wiley and Sons, New York, USAGoogle Scholar