论文标题
局部二次光谱和协方差矩阵估计
Local Quadratic Spectral and Covariance Matrix Estimation
论文作者
论文摘要
重新审视多元时间序列的光谱密度矩阵$ f（w）$的问题，特别关注频率$ w = 0 $和$ w =π$。认识到在这两个边界点处的光谱密度矩阵的条目是实现的，我们提出了一个由多变量周期图的真实部分的局部多项式回归构建的新估计器。 $ w = 0 $的情况非常重要，因为$ f（0）$与样本平均值的大样本协方差矩阵相关联；因此，估计$ f（0）$对于对平均值进行任何统计推断至关重要。我们通过理论和模拟探索本地多项式估计器的特性，并讨论通货膨胀和失业的应用。
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 large-sample covariance matrix of the sample mean; hence, estimating $f(0)$ is crucial in order to conduct any sort of statistical inference on the mean. We explore the properties of the local polynomial estimator through theory and simulations, and discuss an application to inflation and unemployment.
