Periodogram Analysis and Variance Fluctuations
Laurence J. Herbst · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1963
SUMMARY Two problems in the subject of time-series analysis are considered: (A) the effect of fluctuating variances on the periodogram of a set of independent Gaussian data with zero means; (B) the possibility of using the periodogram of squares of independent Gaussian data with zero means as a tool in the Fourier analysis of the variances of the data. The basic effect of fluctuating variances on the periodogram is to introduce correlations (expressible in terms of the Fourier coefficients of the variance) which do not decrease as the sample size increases. The periodogram of squares of independent Gaussian data with zero means is shown to be an appropriate tool in the Fourier analysis of the variances.