ASYMPTOTIC ANALYSIS ABOUT THE PERIODOGRAM OF A GENERAL CLASS OF TIME SERIES MODELS WITH SPECTRAL SUPPORTSON LINES NOT PARALLEL TO THE MAIN DIAGONAL

The aim of this paper is to make inference about a general class of time series models including fractional Brownian motion. The spectral of these processes is supported on lines not parallel to the diagonal T1(x) = x, Tj(x) = αjx ± βj, j = 2,...,m, in spectral square [0, 2π) × [0, 2π), and this class includes stationary, cyclostationary, almost cyclostationary time series and specially fractional Brownian motions. First, the periodogram of these processes is defined and auxiliary operator is applied to explore the distribution of the periodogram. Then the asymptotical estimation for the spectral density function is proposed and asymptotical Wishart function is found. Finally, the validity of the theoretical results is studied using simulated data sets. © 2022 The Author(s).