Theoretical Confidence Level Problems with Confidence Intervals for the Spectrum of a Time Series

Posted: 20 Jan 1997

See all articles by Jon Faust

Jon Faust

Board of Governors of the Federal Reserve System

Date Written: December 1996

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.

JEL Classification: C10, C32

Suggested Citation

Faust, Jon, Theoretical Confidence Level Problems with Confidence Intervals for the Spectrum of a Time Series (December 1996). Available at SSRN: https://ssrn.com/abstract=3657

Jon Faust (Contact Author)

Board of Governors of the Federal Reserve System ( email )

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