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On the convergence of finite linear predictors of stationary processes. (English) Zbl 0676.62070

Summary: It is shown that the finite linear least-squares predictor of a multivariate stationary process converges to its Kolmogorov-Wiener predictor at an exponential rate, provided that the entries of its spectral density matrix are smooth functions. Also, the same rate of convergence holds for the partial sums of the Kolmogorov-Wiener predictor.

MSC:

62M20 Inference from stochastic processes and prediction
60G25 Prediction theory (aspects of stochastic processes)
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