Econometrics 2013, 1(1), 1-31; doi:10.3390/econometrics1010001
Article

On Diagnostic Checking of Vector ARMA-GARCH Models with Gaussian and Student-t Innovations

Booth School of Business, University of Chicago, 5807 South Woodlawn Avenue, Chicago,IL 60637, USA
* Author to whom correspondence should be addressed.
Received: 15 January 2013; in revised form: 9 March 2013 / Accepted: 14 March 2013 / Published: 4 April 2013
(This article belongs to the Special Issue Econometric Model Selection)
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Abstract: This paper focuses on the diagnostic checking of vector ARMA (VARMA) models with multivariate GARCH errors. For a fitted VARMA-GARCH model with Gaussian or Student-t innovations, we derive the asymptotic distributions of autocorrelation matrices of the cross-product vector of standardized residuals. This is different from the traditional approach that employs only the squared series of standardized residuals. We then study two portmanteau statistics, called Q1(M) and Q2(M), for model checking. A residual-based bootstrap method is provided and demonstrated as an effective way to approximate the diagnostic checking statistics. Simulations are used to compare the performance of the proposed statistics with other methods available in the literature. In addition, we also investigate the effect of GARCH shocks on checking a fitted VARMA model. Empirical sizes and powers of the proposed statistics are investigated and the results suggest a procedure of using jointly Q1(M) and Q2(M) in diagnostic checking. The bivariate time series of FTSE 100 and DAX index returns is used to illustrate the performance of the proposed portmanteau statistics. The results show that it is important to consider the cross-product series of standardized residuals and GARCH effects in model checking.
Keywords: Vector autoregressive moving-average process; multivariate GARCH model; asymptotic distribution; portmanteau statistic; model checking; heavy tail; multivariate time series; bootstrap

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MDPI and ACS Style

Wang, Y.; Tsay, R.S. On Diagnostic Checking of Vector ARMA-GARCH Models with Gaussian and Student-t Innovations. Econometrics 2013, 1, 1-31.

AMA Style

Wang Y, Tsay RS. On Diagnostic Checking of Vector ARMA-GARCH Models with Gaussian and Student-t Innovations. Econometrics. 2013; 1(1):1-31.

Chicago/Turabian Style

Wang, Yongning; Tsay, Ruey S. 2013. "On Diagnostic Checking of Vector ARMA-GARCH Models with Gaussian and Student-t Innovations." Econometrics 1, no. 1: 1-31.

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