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Prediction in invertible linear processes

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  • Schick, Anton
  • Wefelmeyer, Wolfgang

Abstract

We construct root-n consistent plug-in estimators for conditional expectations of the form E(h(Xn+1,...,Xn+m)X1,...,Xn) in invertible linear processes. More specifically, we prove a Bahadur-type representation for such estimators, uniformly over certain classes of not necessarily bounded functions h. We obtain in particular a uniformly root-n consistent estimator for the m-dimensional conditional distribution function. The proof uses empirical process techniques.

Suggested Citation

  • Schick, Anton & Wefelmeyer, Wolfgang, 2007. "Prediction in invertible linear processes," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1322-1331, July.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:12:p:1322-1331
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    References listed on IDEAS

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    1. Tran, Lanh Tat, 1992. "Kernel density estimation for linear processes," Stochastic Processes and their Applications, Elsevier, vol. 41(2), pages 281-296, June.
    2. Masry, Elias, 1989. "Nonparametric estimation of conditional probability densities and expectations of stationary processes: strong consistency and rates," Stochastic Processes and their Applications, Elsevier, vol. 32(1), pages 109-127, June.
    3. Roussas, George G., 1991. "Recursive estimation of the transition distribution function of a Markov process: A symptotic normality," Statistics & Probability Letters, Elsevier, vol. 11(5), pages 435-447, May.
    4. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
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