The Autoregressive Method: A Method of Approximating and Estimating Positive Functions.

摘要

The Fourier transform was considered for a positive function f(.) (or its sample Fourier transform) as a possibly complex covariance function of a hypothetical stationary complex-valued time series. This models time series by an autoregressive process of order p whose spectral density approximates (or estimates) the function f(.). The equivalence of this interpretation with the theory of orthogonal polynomials on the unit circle was studied; also the consistency of the autoregressive estimator as p increases with the sample size.