Model identification via total Frobenius norm of multivariate spectra
研究用Frobenius范数的积分衡量两个多元谱的差异，用于拟合时间序列模型、检验残差是否为白噪声，并发展协整秩检验，模拟和实证表明能实时拟合中高维结构时间序列。
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 case of structural time series models is addressed, wherein co-integration rank testing is formally developed. Both applications are studied through simulation studies and time series data. The numerical results show that the proposed estimator can fit moderate- to large-dimensional structural timeseries in real time.