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Model identification via total Frobenius norm of multivariate spectra

Author

Listed:
  • Tucker S. McElroy
  • Anindya Roy

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.

Suggested Citation

  • Tucker S. McElroy & Anindya Roy, 2022. "Model identification via total Frobenius norm of multivariate spectra," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 473-495, April.
    • Handle: RePEc:bla:jorssb:v:84:y:2022:i:2:p:473-495
    DOI: 10.1111/rssb.12480
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    References listed on IDEAS

    as
    1. Tucker S McElroy & Agnieszka Jach, 2019. "Testing collinearity of vector time series," The Econometrics Journal, Royal Economic Society, vol. 22(2), pages 97-116.
    2. Tucker McElroy, 2017. "Multivariate Seasonal Adjustment, Economic Identities, and Seasonal Taxonomy," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 611-625, October.
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    5. McElroy, Tucker S. & Politis, Dimitris N., 2014. "Spectral density and spectral distribution inference for long memory time series via fixed-b asymptotics," Journal of Econometrics, Elsevier, vol. 182(1), pages 211-225.
    6. Tucker McElroy & Thomas Trimbur, 2015. "Signal Extraction for Non-Stationary Multivariate Time Series with Illustrations for Trend Inflation," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 209-227, March.
    7. Pena D. & Rodriguez J., 2002. "A Powerful Portmanteau Test of Lack of Fit for Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 601-610, June.
    8. Deo, Rohit S. & Chen, Willa W., 2000. "On the integral of the squared periodogram," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 159-176, January.
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    13. Douglas Rivers & Quang Vuong, 2002. "Model selection tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 1-39, June.
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