Analysis Of A Long Memory Circular Convolution Model

Abstract

A stochastic model, the product of a circulant matrix and a random normal vector, is shown to produce an evolutive long memory time series with a power law spectral density. The distribution of the time series, a beta location scale family of distributions, provides a connection to the unit centered spherical distribution and directional statistics. The eigenanalysis of the deterministic circulant matrix is shown to provide estimates of the discrete Fourier spectral trend, the intrinsic dimension, the probability density shape parameter of the resulting time series, the condition number of the matrix and a principle component analysis. Examples of the R code, used as the constructive exploratory element of the work are given as constructive elements of the paper. The R code may be copied, pastedinto a R editor, and explored.