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Strongly Consistent Nonparametric Forecasting and Regression for Stationary Ergodic Sequences

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  • Yakowitz, Sidney
  • Györfi, László
  • Kieffer, John
  • Morvai, Gusztáv

Abstract

Let {(Xi, Yi)} be a stationary ergodic time series with (X, Y) values in the product space Rd[circle times operator]R. This study offers what is believed to be the first strongly consistent (with respect to pointwise, least-squares, and uniform distance) algorithm for inferring m(x)=E[Y0  X0=x] under the presumption that m(x) is uniformly Lipschitz continuous. Auto-regression, or forecasting, is an important special case, and as such our work extends the literature of nonparametric, nonlinear forecasting by circumventing customary mixing assumptions. The work is motivated by a time series model in stochastic finance and by perspectives of its contribution to the issues of universal time series estimation.

Suggested Citation

  • Yakowitz, Sidney & Györfi, László & Kieffer, John & Morvai, Gusztáv, 1999. "Strongly Consistent Nonparametric Forecasting and Regression for Stationary Ergodic Sequences," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 24-41, October.
    • Handle: RePEc:eee:jmvana:v:71:y:1999:i:1:p:24-41
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    References listed on IDEAS

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    1. Yakowitz, Sid, 1993. "Nearest neighbor regression estimation for null-recurrent Markov time series," Stochastic Processes and their Applications, Elsevier, vol. 48(2), pages 311-318, November.
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    Cited by:

    1. Guerre, 2004. "Design-Adaptive Pointwise Nonparametric Regression Estimation For Recurrent Markov Time Series," Econometrics 0411007, University Library of Munich, Germany.
    2. Sancetta, A., 2005. "Forecasting Distributions with Experts Advice," Cambridge Working Papers in Economics 0517, Faculty of Economics, University of Cambridge.
    3. Didi Sultana & Louani Djamal, 2014. "Asymptotic results for the regression function estimate on continuous time stationary and ergodic data," Statistics & Risk Modeling, De Gruyter, vol. 31(2), pages 129-150, June.

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