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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.
Full paper (239 KB PDF)
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Full paper (256 KB Postscript)
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