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Consistent estimation of a general nonparametric regression function in time series

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  • Linton, Oliver
  • Sancetta, Alessio

Abstract

We propose an estimator of the conditional distribution of XtXt-1,Xt-2,..., and the corresponding regression function , where the conditioning set is of infinite order. We establish consistency of our estimator under stationarity and ergodicity conditions plus a mild smoothness condition.

Suggested Citation

  • Linton, Oliver & Sancetta, Alessio, 2009. "Consistent estimation of a general nonparametric regression function in time series," Journal of Econometrics, Elsevier, vol. 152(1), pages 70-78, September.
    • Handle: RePEc:eee:econom:v:152:y:2009:i:1:p:70-78
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    References listed on IDEAS

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    1. Masry, Elias, 2005. "Nonparametric regression estimation for dependent functional data: asymptotic normality," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 155-177, January.
    2. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    3. Sancetta, Alessio, 2009. "Nearest neighbor conditional estimation for Harris recurrent Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2224-2236, November.
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    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.
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    10. Pagan, Adrian & Ullah, Aman, 1988. "The Econometric Analysis of Models with Risk Terms," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(2), pages 87-105, April.
    11. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    12. Linton, Oliver & Perron, Benoit, 2003. "The Shape of the Risk Premium: Evidence from a Semiparametric Generalized Autoregressive Conditional Heteroscedasticity Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 354-367, July.
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    Cited by:

    1. Seok Young Hong & Oliver Linton, 2016. "Asymptotic properties of a Nadaraya-Watson type estimator for regression functions of in?finite order," CeMMAP working papers CWP53/16, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Hong, Seok Young & Linton, Oliver, 2020. "Nonparametric estimation of infinite order regression and its application to the risk-return tradeoff," Journal of Econometrics, Elsevier, vol. 219(2), pages 389-424.
    3. Li, Degui & Lu, Zudi & Linton, Oliver, 2012. "Local Linear Fitting Under Near Epoch Dependence: Uniform Consistency With Convergence Rates," Econometric Theory, Cambridge University Press, vol. 28(5), pages 935-958, October.
    4. Battey, Heather & Sancetta, Alessio, 2013. "Conditional estimation for dependent functional data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 1-17.
    5. Degui Li & Oliver Linton & Zudi Lu, 2012. "A Flexible Semiparametric Model for Time Series," Monash Econometrics and Business Statistics Working Papers 17/12, Monash University, Department of Econometrics and Business Statistics.
    6. repec:awi:wpaper:0473 is not listed on IDEAS
    7. Li, Degui & Lu, Zudi & Linton, Oliver, 2010. "Loch linear fitting under near epoch dependence: uniform consistency with convergence rate," LSE Research Online Documents on Economics 58160, London School of Economics and Political Science, LSE Library.
    8. Li, Degui & Linton, Oliver & Lu, Zudi, 2015. "A flexible semiparametric forecasting model for time series," Journal of Econometrics, Elsevier, vol. 187(1), pages 345-357.
    9. Seok Young Hong & Oliver Linton, 2016. "Asymptotic properties of a Nadaraya-Watson type estimator for regression functions of in finite order," CeMMAP working papers 53/16, Institute for Fiscal Studies.

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    Kernel Regression Time series;

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