Asymptotic Properties of the Wiener–Kolmogorov Predictor. I
Rupal J. Bhansali · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1974
Summary “Windowed” estimates of the spectral density function are used to carry out the factorization of the sample spectral density function and hence estimate the Wiener-Kolmogorov prediction coefficients. Expressions are derived for the asymptotic mean and variance of all the statistics necessary to estimate the predictor. The covariances and asymptotic normality of these estimates are also investigated. In particular, an expression for the asymptotic mean-square error or predicting one step, and more than one step, ahead is given.