The Prediction Expression of Multidimensional Stationary Sequence and Rosenblatt's Speculation

Abstract:

      In this pape we obtain a linear predictor and its error for a multidimensional, discrete parameter, full-rank and regular stationary stochastic process (S. P.) having a spectral density matrix f(λ), which mets some conditions. An example which shows that Szego-Kolmogorov's Theorem for the prediction error with lag l in terms f(λ):σ₁²=2πexp{1/(2π)∫_-x^xlogf(λ)dλ},(1) can't be formally kept true in matrix form is given.