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高维谱密度矩阵的统计推断AI 解读

The spectral density matrix is a fundamental object of interest in time series analysis, and it encodes both contemporary and dynamic linear relationships between component processes of the multivariate system. In this paper we develop novel inference procedures for the spectral density matrix in the high-dimensional setting. Specifically, we introduce a new global testing procedure to test the nullity of the cross-spectral density for a given set of frequencies and across…

局部二次谱密度矩阵与协方差矩阵估计AI 解读

The problem of estimating the spectral density matrix $f(w)$ of a multivariate time series is revisited with special focus on the frequencies $w=0$ and $w=π$. Recognizing that the entries of the spectral density matrix at these two boundary points are real-valued, we propose a new estimator constructed from a local polynomial regression of the real portion of the multivariate periodogram. The case $w=0$ is of particular importance, since $f(0)$ is associated with the…

降秩与协整向量自回归的约束参数化AI 解读

The paper provides a parametrization of Vector Autoregression (VAR) that enables one to look at the parameters associated with unit root dynamics and those associated with stable dynamics separately. The task is achieved via a novel factorization of the VAR polynomial that partitions the polynomial spectrum into unit root and stable and zero roots via polynomial factors. The proposed factorization adds to the literature of spectral factorization of matrix polynomials. The…