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On a property of the finite Fourier partial sums process

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  • Kulperger, R. J.

Abstract

Let {Xn; n [greater-or-equal, slanted] 1} be a stationary sequence of random variables with finite variance, and dN([lambda]) be the finite Fourier transform based on data X1, ... , XN. Let AN(t), 0 [less-than-or-equals, slant] t [less-than-or-equals, slant] 1 be the normalized process of partial sums of the finite Fourier transforms. In general, AN does not converge to a Gaussian process, unless the process {X} is Gaussian. This has some implications in goodness of fit checks for time series. This partial sum formally looks like a discrete approximation to the process that converges to the Cramer representation. The difference between the process AN and the Cramer process does not converge to zero.

Suggested Citation

  • Kulperger, R. J., 1997. "On a property of the finite Fourier partial sums process," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 101-107, September.
    • Handle: RePEc:eee:stapro:v:35:y:1997:i:2:p:101-107
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    References listed on IDEAS

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    1. Reg Kulperger, 1985. "On An Optimality Property Of Whittle'S Gaussian Estimate Of The Parameter Of The Spectrum Of A Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(4), pages 253-259, July.
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