On the convergence of finite linear predictors of stationary processes

DOI10.1016/0047-259X(89)90033-XzbMath0676.62070MaRDI QIDQ1122914

Mohsen Pourahmadi

Publication date: 1989

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

smoothprediction errorpartial sumsanalyticexponential rate of convergencespectral density matrixmultivariate stationary processfinite linear least-squares predictorKolmogorov-Wiener predictor

Mathematics Subject Classification ID

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

Related Items (7)

Baxter's inequality and convergence of finite predictors of multivariate stochastic processes ⋮ Mixed‐Norm Spaces and Prediction of SαS Moving Averages ⋮ Convergence of the best linear predictor of a weakly stationary random field ⋮ Model selection for high-dimensional linear regression with dependent observations ⋮ The mixing rate of a stationary multivariate process ⋮ Hölder classes of vector-valued functions and convergence of the best predictor ⋮ Linear prediction of long-range dependent time series

Cites Work

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• The prediction theory of multivariate stochastic processes. I. The regularity condition. - II. The linear predictor
• On the mean convergence of the best linear interpolator of multivariate stationary stochastic processes
• Autocorrelation, autoregression and autoregressive approximation
• A note on the degree of approximation of Fourier series
• A matricial extension of the Helson-Szegö theorem and its application in multivariate prediction
• Consistent autoregressive spectral estimates
• The Helson-Sarason-Szego Theorem and the Abel Summability of the Series for the Predictor
• An Asymptotic Result for the Finite Predictor.
• On the Bilateral Linear Predictor for Minimal Stationary Stochastic Processes
• Asymptotic Estimates for the Finite Predictor.
• An Extension of a Theorem of G. Szego and Its Application to the Study of Stochastic Processes

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