Hypothesis testing for the precision matrix of high-dimensional periodic vector autoregressive model

doi:10.3969/j.issn.1000-5641.2023.02.007

Abstract

Abstract:

The precision (inverse covariance) matrix generated by the periodic vector autoregressive model is a sparse block tridiagonal matrix. Based on this precision matrix, a new block trace function is proposed for testing the equality of block traces of two precision matrices, the asymptotic behavior under the null hypothesis is investigated. Numerical experiments show that the proposed testing procedure has both appropriate size and good power.

Key words: hypothesis testing, periodic vector autoregressive model, precision matrix, block tridiagonal matrix

CLC Number:

O212.1

Jin ZOU. Hypothesis testing for the precision matrix of high-dimensional periodic vector autoregressive model[J]. Journal of East China Normal University(Natural Science), 2023, 2023(2): 48-59.

Figures/Tables 2

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(d, T, n)	ASL				势函数值
(d, T, n)	LRT	CLRT	UVW	ICT	LRT	CLRT	UVW	ICT
(2, 4, 300)	0.056	0.072	0.052	0.061	0.906	0.906	0.114	0.990
(2, 10, 300)	0.088	0.064	0.054	0.053	0.896	0.894	0.882	0.863
(10, 5, 300)	0.480	0.067	0.052	0.050	0.841	0.851	0.812	0.845
(10, 30, 300)			0.045	0.047			0.988	0.978
(10, 40, 300)			0.044	0.049			0.911	0.967
(30, 40, 1000)			0.051	0.048			0.776	0.883
(100, 20, 1000)			0.034	0.041			0.671	0.783

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