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Volume 40, Issue 1
On a Partially Non-Stationary Vector AR Model with Vector GARCH Noises: Estimation and Testing

Chor-yiu Sin, Zichuan Mi & Shiqing Ling

DOI: 10.4208/cmr.2023-0005

Commun. Math. Res., 40 (2024), pp. 64-101.

Published online: 2023-12

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  • Abstract

 This paper studies a partially nonstationary vector autoregressive (VAR) model with vector GARCH noises. We study the full rank and the reduced rank quasi-maximum likelihood estimators (QMLE) of parameters in the model. It is shown that both QMLE of long-run parameters asymptotically converge to a functional of two correlated vector Brownian motions. Based these, the likelihood ratio (LR) test statistic for cointegration rank is shown to be a functional of the standard Brownian motion and normal vector, asymptotically. As far as we know, our test is new in the literature. The critical values of the LR test are simulated via the Monte Carlo method. The performance of this test in finite samples is examined through Monte Carlo experiments. We apply our approach to an empirical example of three interest rates.

  • Keywords

Vector AR model, cointegration, full rank estimation, vector GARCH process, partially nonstationary, reduced rank estimation.

  • AMS Subject Headings

62M10, 37M10, 91B84

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-40-64, author = {Sin , Chor-yiuMi , Zichuan and Ling , Shiqing}, title = {On a Partially Non-Stationary Vector AR Model with Vector GARCH Noises: Estimation and Testing}, journal = {Communications in Mathematical Research }, year = {2023}, volume = {40}, number = {1}, pages = {64--101}, abstract = {

 This paper studies a partially nonstationary vector autoregressive (VAR) model with vector GARCH noises. We study the full rank and the reduced rank quasi-maximum likelihood estimators (QMLE) of parameters in the model. It is shown that both QMLE of long-run parameters asymptotically converge to a functional of two correlated vector Brownian motions. Based these, the likelihood ratio (LR) test statistic for cointegration rank is shown to be a functional of the standard Brownian motion and normal vector, asymptotically. As far as we know, our test is new in the literature. The critical values of the LR test are simulated via the Monte Carlo method. The performance of this test in finite samples is examined through Monte Carlo experiments. We apply our approach to an empirical example of three interest rates.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2023-0005}, url = {http://global-sci.org/intro/article_detail/cmr/22282.html} }
TY - JOUR T1 - On a Partially Non-Stationary Vector AR Model with Vector GARCH Noises: Estimation and Testing AU - Sin , Chor-yiu AU - Mi , Zichuan AU - Ling , Shiqing JO - Communications in Mathematical Research VL - 1 SP - 64 EP - 101 PY - 2023 DA - 2023/12 SN - 40 DO - http://doi.org/10.4208/cmr.2023-0005 UR - https://global-sci.org/intro/article_detail/cmr/22282.html KW - Vector AR model, cointegration, full rank estimation, vector GARCH process, partially nonstationary, reduced rank estimation. AB -

 This paper studies a partially nonstationary vector autoregressive (VAR) model with vector GARCH noises. We study the full rank and the reduced rank quasi-maximum likelihood estimators (QMLE) of parameters in the model. It is shown that both QMLE of long-run parameters asymptotically converge to a functional of two correlated vector Brownian motions. Based these, the likelihood ratio (LR) test statistic for cointegration rank is shown to be a functional of the standard Brownian motion and normal vector, asymptotically. As far as we know, our test is new in the literature. The critical values of the LR test are simulated via the Monte Carlo method. The performance of this test in finite samples is examined through Monte Carlo experiments. We apply our approach to an empirical example of three interest rates.

Chor-yiu Sin, Zichuan Mi & Shiqing Ling. (2023). On a Partially Non-Stationary Vector AR Model with Vector GARCH Noises: Estimation and Testing. Communications in Mathematical Research . 40 (1). 64-101. doi:10.4208/cmr.2023-0005
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