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Mixed-Norm Spaces and Prediction of SαS Moving Averages

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  • Raymond Cheng
  • Charles B. Harris

Abstract

type="main" xml:id="jtsa12134-abs-0001"> Suppose that Z k k = − ∞ ∞ is an i.i.d. symmetric α-stable noise, 1 > α > 2, and consider the moving average process X k k = − ∞ ∞ given by X k = ∑ j = 0 ∞ a j Z k − j . Conditions are obtained for the convergence rate of the moving average series, as well as that of the inverted (autoregressive) representation Z k = ∑ j = 0 ∞ c j X k − j . These conditions are expressed in terms of the associated function F ( z ) = ∑ j = 0 ∞ a j z j and its reciprocal belonging to certain mixed-norm spaces of functions on the open unit disc. Properties of these spaces are explored. Criteria are also derived for the rate of mixing in a certain sense.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:6:p:853-875
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    References listed on IDEAS

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    5. 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.
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