On a property of the finite Fourier partial sums process

✍ Scribed by R.J. Kulperger

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 315 KB
• Volume: 35
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(97)00002-3

✦ Synopsis

Let {X,; n~>l} be a stationary sequence of random variables with finite variance, and dN(2) be the finite Fourier transform based on data Xi .... ,AN. Let AN(t), 0~<t~<l 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 Cramrr representation. The difference between the process AN and the Cramrr process does not converge to zero.