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Hölder classes of vector-valued functions and convergence of the best predictor

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  • Cheng, R.

Abstract

The Hölder classes [Lambda]a of vector-valued functions are defined. The functions in each space [Lambda]a are completely characterized by conditions concerning the decay of their Fourier coefficients, their smoothness, and their approximability by polynomials. It is shown that, in some sense, [Lambda]a is closed under multiplication, inversion, and factorization. These ideas are applied to a prediction problem for multivariate stationary processes. Specifically, spectral criteria are derived for the convergence rate of the series representation for the best linear predictor.

Suggested Citation

  • Cheng, R., 1992. "Hölder classes of vector-valued functions and convergence of the best predictor," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 110-129, July.
    • Handle: RePEc:eee:jmvana:v:42:y:1992:i:1:p:110-129
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    Cited by:

    1. Raymond Cheng & Charles B. Harris, 2015. "Mixed-Norm Spaces and Prediction of SαS Moving Averages," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 853-875, November.

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