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基于多元谱积分 Frobenius 范数的模型识别AI 解读

Abstract We study the integral of the Frobenius norm as a measure of the discrepancy between two multivariate spectra. Such a measure can be used to fit time series models, and ensures proximity between model and process at all frequencies of the spectral density. We develop new asymptotic results for linear and quadratic functionals of the periodogram, and apply the integrated Frobenius norm to fit time series models and test whether model residuals are white noise. The…

向量时间序列共线性检验AI 解读

Summary We investigate the collinearity of vector time series in the frequency domain, by examining the rank of the spectral density matrix at a given frequency of interest. Rank reduction corresponds to collinearity at the given frequency. When the time series is nonstationary and has been differenced to stationarity, collinearity corresponds to co-integration at a particular frequency. We examine rank through the Schur complements of the spectral density matrix, testing…