For large multivariate models of generalized autoregressive conditional heteroskedasticity (GARCH), it is important to reduce the number of parameters to cope with the 'curse of dimensionality'. Recently, Laurent, Rombouts and Violante (2014 "Multivariate Rotated ARCH Models"Journal of Econometrics 179: 16-30) developed the rotated multivariate GARCH model, which focuses on the parameters for standardized variables. This paper extends the rotated multivariate GARCH model by considering a hyper-rotation, which uses a more flexible structure for the rotation matrix. The paper shows an alternative representation based on a random coefficient vector autoregressive and moving-average (VARMA) process, and provides the regularity conditions for the consistency and asymptotic normality of the quasi-maximum likelihood (QML) estimator for VARMA with hyper-rotated multivariate GARCH. The paper investigates the finite sample properties of the QML estimator for the new model. Empirical results for four exchange rate returns show the new specifications works satisfactory for reducing the number of parameters.
Bibliographical noteJEL Classification: C13; C32
Funding source: Japan Society for the Promotion of Science Award Identifier / Grant number: 19K01594
The authors are most grateful to Yoshihisa Baba, Chialin Chang, Laurent Pauwels, and anonymous two reviewers for very helpful comments and suggestions. The first author acknowledges the financial support of the Japan Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science (JSPS 19K01594), and the Australian Academy of Science. The second author wishes to thank the Australian Research Council and the Ministry of Science and Technology (MOST), Taiwan.
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