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Design-Adaptive Pointwise Nonparametric Regression Estimation for Recurrent Markov Time Series

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  • Emmanuel Guerre

    (Crest)

Abstract

A general framework is proposed for (auto)regression nonparametric estimationof recurrent time series in a class of Hilbert Markov processes with a Lipschitzconditional mean. This includes various nonstationarities by relaxing usual dependenceassumptions as mixing or ergodicity, which are replaced with recurrence. The cornerstoneof design-adaptation is a data-driven bandwidth choice based on an empirical biasvariance tradeoff, giving rise to a random consistency rate for a uniform kernel estimator.The estimator converges with this random rate, which is the optimal minimaxrandom rate over the considered class of recurrent time series. Extensions to general kernelestimators are investigated. For weak dependent time-series, the order of the randomrate coincides with the deterministic minimax rate previously derived. New deterministicestimation rates are obtained for modified Box-Cox transformations of Random Walks.

Suggested Citation

  • Emmanuel Guerre, 2004. "Design-Adaptive Pointwise Nonparametric Regression Estimation for Recurrent Markov Time Series," Working Papers 2004-22, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2004-22
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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.
    2. E. Guerre & J. Maës, 1998. "Optimal Rate for Nonparametric Estimation in Deterministic Dynamical Systems," Statistical Inference for Stochastic Processes, Springer, vol. 1(2), pages 157-173, May.
    3. repec:crs:wpaper:9806 is not listed on IDEAS
    4. Guerre, Emmanuel, 2000. "Design Adaptive Nearest Neighbor Regression Estimation," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 219-244, November.
    5. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
    6. Alain Berlinet & Gérard Biau, 2001. "Minimax Bounds in Nonparametric Estimation of Multidimensional Deterministic Dynamical Systems," Statistical Inference for Stochastic Processes, Springer, vol. 4(3), pages 229-248, October.
    7. 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.
    8. Robinson, Peter M., 1997. "Large-sample inference for nonparametric regression with dependent errors," LSE Research Online Documents on Economics 302, London School of Economics and Political Science, LSE Library.
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    Citations

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    Cited by:

    1. Federico M Bandi & Valentina Corradi & Daniel Wilhelm, 2016. "Possibly Nonstationary Cross-Validation," CeMMAP working papers CWP11/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Scholz, Michael & Nielsen, Jens Perch & Sperlich, Stefan, 2015. "Nonparametric prediction of stock returns based on yearly data: The long-term view," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 143-155.
    3. Peter C. B. Phillips & Donggyu Sul, 2007. "Transition Modeling and Econometric Convergence Tests," Econometrica, Econometric Society, vol. 75(6), pages 1771-1855, November.
    4. Federico M Bandi & Valentina Corradi & Daniel Wilhelm, 2016. "Possibly Nonstationary Cross-Validation," CeMMAP working papers 11/16, Institute for Fiscal Studies.
    5. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(3), pages 710-738, June.
    6. Peter C. B. Phillips & Donggyu Sul, 2009. "Economic transition and growth," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(7), pages 1153-1185.
    7. Bandi, Federico & Corradi, Valentina & Moloche, Guillermo, 2009. "Bandwidth selection for continuous-time Markov processes," MPRA Paper 43682, University Library of Munich, Germany.
    8. Kasparis, Ioannis & Phillips, Peter C.B., 2012. "Dynamic misspecification in nonparametric cointegrating regression," Journal of Econometrics, Elsevier, vol. 168(2), pages 270-284.
    9. Delattre, Sylvain & Gaïffas, Stéphane, 2011. "Nonparametric regression with martingale increment errors," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2899-2924.
    10. Phillips, Peter C.B., 2009. "Local Limit Theory And Spurious Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1466-1497, December.
    11. Schienle, Melanie, 2011. "Nonparametric nonstationary regression with many covariates," SFB 649 Discussion Papers 2011-076, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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