On a property of the finite Fourier partial sums process

R. J. Kulperger

Statistics & Probability Letters, 1997, vol. 35, issue 2, 101-107

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.

Keywords: Finite; Fourier; transform; Partial; sums; Weak; convergence; Non-Gaussian; Distribution; free (search for similar items in EconPapers)
Date: 1997
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