Model identification via total Frobenius norm of multivariate spectra

Tucker McElroy () and Anindya Roy

Journal of the Royal Statistical Society Series B, 2022, vol. 84, issue 2, 473-495

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—this is more demanding than Kullback–Leibler discrepancy, which is instead related to one‐step ahead forecasting performance. We develop new asymptotic results for linear and quadratic functionals of the periodogram, and make two applications of the integrated Frobenius norm: (i) fitting time series models, and (ii) testing whether model residuals are white noise. Model fitting results are further specialized to the case of structural time series models, wherein co‐integration rank testing is formally developed. Both applications are studied through simulation studies, as well as illustrations on inflation and construction data. The numerical results show that the proposed estimator can fit moderate‐ to large‐dimensional structural time series in real time, an option that is lacking in current literature.

Date: 2022
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