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用一组标量偏自相关系数刻画协方差矩阵AI 解读

It has been shown that the autocovariance matrices of a stationary multivariate time series can be uniquely characterized by a sequence of the normalized partial autocorrelation matrices having singular values less than one. In this note, we show that the same autocovariance matrices can be also uniquely characterized by a set of sequences of scalar partial autocorrelation coefficients whose magnitudes are all less than one.

自回归拟合与周期图的关系及其应用AI 解读

The relation between fitting autoregression and periodogram is herein presented. More specifically, the asymptotic error covariance matrices of the estimates of the autoregressive parameters using Yule-Walker equations are expressed in terms of the periodogram. These expressions permit the immediate calculation of the error covariance matrices for various time series problems including the autoregressive spectral estimation and fitting autoregression to the data with…