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Frequency domain principal components estimation of fractionally cointegrated processes

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  • Morana, Claudio

Abstract

In this paper we study the zero frequency spectral properties of fractionally cointegrated long memory processes and introduce a new frequency domain principal components estimator of the cointegration space and the factor loading matrix for the long memory factors. We find that for fractionally differenced (fractionally) cointegrated processes the squared multiple coherence at the zero frequency is equal to one, the spectral density matrix at the zero frequency is singular, and the factor loading and cointegrating matrices can be obtained from the eigenvectors of the spectral matrix at the zero frequency, associated with the positive and zero roots, respectively. A Monte Carlo simulation reveals that the proposed principal components estimator has already good properties with relatively small sample sizes. JEL Classification: C22

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  • Morana, Claudio, 2004. "Frequency domain principal components estimation of fractionally cointegrated processes," Working Paper Series 321, European Central Bank.
    • Handle: RePEc:ecb:ecbwps:2004321
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    Citations

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    Cited by:

    1. Nuno Cassola & Claudio Morana, 2008. "Modeling Short-Term Interest Rate Spreads in the Euro Money Market," International Journal of Central Banking, International Journal of Central Banking, vol. 4(4), pages 1-37, December.
    2. Claudio Morana, 2007. "A structural common factor approach to core inflation estimation and forecasting," Applied Economics Letters, Taylor & Francis Journals, vol. 14(3), pages 163-169.
    3. Claudio Morana, 2010. "Heteroskedastic Factor Vector Autoregressive Estimation of Persistent and Non Persistent Processes Subject to Structural Breaks," ICER Working Papers - Applied Mathematics Series 36-2010, ICER - International Centre for Economic Research.
    4. Claudio Morana & Fabio Cesare Bagliano, 2007. "Inflation and monetary dynamics in the USA: a quantity-theory approach," Applied Economics, Taylor & Francis Journals, vol. 39(2), pages 229-244.
    5. Claudio Morana & Andrea Beltratti, 2006. "Structural breaks and common factors in the volatility of the Fama-French factor portfolios," Applied Financial Economics, Taylor & Francis Journals, vol. 16(14), pages 1059-1073.
    6. Cassola, Nuno & Morana, Claudio, 2010. "Comovements in volatility in the euro money market," Journal of International Money and Finance, Elsevier, vol. 29(3), pages 525-539, April.
    7. Morana, Claudio, 2006. "A small scale macroeconometric model for the Euro-12 area," Economic Modelling, Elsevier, vol. 23(3), pages 391-426, May.
    8. Beltratti, A. & Morana, C., 2006. "Breaks and persistency: macroeconomic causes of stock market volatility," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 151-177.
    9. Tobias Hartl & Roland Jucknewitz, 2022. "Approximate state space modelling of unobserved fractional components," Econometric Reviews, Taylor & Francis Journals, vol. 41(1), pages 75-98, January.
    10. Tobias Hartl & Roland Weigand, 2018. "Multivariate Fractional Components Analysis," Papers 1812.09149, arXiv.org, revised Jan 2019.
    11. Eroğlu, Burak Alparslan, 2019. "Wavelet variance ratio cointegration test and wavestrapping," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 298-319.
    12. Morana, Claudio, 2007. "Multivariate modelling of long memory processes with common components," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 919-934, October.
    13. Burak Eroglu, 2017. "Wavelet Variance Ratio Test And Wavestrapping For The Determination Of The Cointegration Rank," Working Papers 1706, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.
    14. Burak Eroglu & Kemal Caglar Gogebakan & Mirza Trokic, 2017. "Fractional Seasonal Variance Ratio Unit Root Tests," Working Papers 1707, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.

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    More about this item

    Keywords

    fractional cointegration; frequency domain; long memory;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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