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A convergence theorem for spectral factorization

Author

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  • Wilson, G. Tunnicliffe

Abstract

This paper presents a convergence theorem for an iterative method of spectral factorization in the context of multivariate prediction theory. It may be viewed as a constructive proof that the factorization exists, using only the analytic results of Hardy space theory.

Suggested Citation

  • Wilson, G. Tunnicliffe, 1978. "A convergence theorem for spectral factorization," Journal of Multivariate Analysis, Elsevier, vol. 8(2), pages 222-232, June.
    • Handle: RePEc:eee:jmvana:v:8:y:1978:i:2:p:222-232
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    Citations

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    Cited by:

    1. Tata Subba Rao & Granville Tunnicliffe Wilson & Granville Tunnicliffe Wilson, 2017. "Spectral Estimation of the Multivariate Impulse Response," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 381-391, March.
    2. Li, Yue & Goodell, John W. & Shen, Dehua, 2021. "Comparing search-engine and social-media attentions in finance research: Evidence from cryptocurrencies," International Review of Economics & Finance, Elsevier, vol. 75(C), pages 723-746.
    3. Yuzo Hosoya & Taro Takimoto, 2010. "A numerical method for factorizing the rational spectral density matrix," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 229-240, July.
    4. Li, Lei M., 2005. "Factorization of moving-average spectral densities by state-space representations and stacking," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 425-438, October.
    5. Torun, Erdost & Chang, Tzu-Pu & Chou, Ray Y., 2020. "Causal relationship between spot and futures prices with multiple time horizons: A nonparametric wavelet Granger causality test," Research in International Business and Finance, Elsevier, vol. 52(C).
    6. Yongjie Zhang & Yue Li & Dehua Shen, 2022. "Investor Attention and the Carbon Emission Markets in China: A Nonparametric Wavelet-Based Causality Test," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(1), pages 123-137, March.
    7. Li, Yue & W. Goodell, John & Shen, Dehua, 2021. "Does happiness forecast implied volatility? Evidence from nonparametric wave-based Granger causality testing," The Quarterly Review of Economics and Finance, Elsevier, vol. 81(C), pages 113-122.

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