The Autoregressive Method: A Method of Approximating and Estimating Positive Functions
STATE UNIV OF NEW YORK AT BUFFALO AMHERST STATISTICAL SCIENCE DIV
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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 model 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.
- Numerical Mathematics