Asymptotic properties of least-squares estimates of parameters of the spectrum of a stationary non-deterministic time-series

Let {x t } (t = 0, ±1, ±2 …) be a stationary non-deterministic time series with E(x 2 t ) < ∞, E(x t ) = 0, and let its spectrum be continuous (strictly absolutely continuous) so that the spectral distribution function is the spectral density function. It is well known that {x t } then has a unique one-sided movingaverage representation where .