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Theoretical confidence level problems with confidence intervals for the spectrum of a time series

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Abstract

Textbook approaches to forming asymptotically justified confidence intervals for the spectrum under very general assumptions were developed by the mid-1970s. This paper shows that under the textbook assumptions, the true confidence level for these intervals does not converge to the asymptotic level, and instead is fixed at zero in all sample sizes. The paper explores necessary conditions for solving this problem, most notably showing that under weak conditions, forming valid confidence intervals requires that one limit consideration to a finite-dimensional time series model.

Suggested Citation

  • Jon Faust, 1996. "Theoretical confidence level problems with confidence intervals for the spectrum of a time series," International Finance Discussion Papers 575, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgif:575
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    File URL: http://www.federalreserve.gov/pubs/ifdp/1996/575/default.htm
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    Cited by:

    1. Dufour, J.M., 2001. "Logique et tests d'hypotheses: reflexions sur les problemes mal poses en econometrie," Cahiers de recherche 2001-15, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing," Cahiers de recherche 16-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. Dufour, Jean-Marie, 2001. "Logique et tests d’hypothèses," L'Actualité Economique, Société Canadienne de Science Economique, vol. 77(2), pages 171-190, juin.
    4. Neville Francis & Michael T. Owyang & Jennifer E. Roush & Riccardo DiCecio, 2014. "A Flexible Finite-Horizon Alternative to Long-Run Restrictions with an Application to Technology Shocks," The Review of Economics and Statistics, MIT Press, vol. 96(4), pages 638-647, October.

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    Keywords

    time series analysis;

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