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Nonparametric regression for locally stationary time series

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  • Michael Vogt
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    Abstract

    In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coecients. We introduce a kernel-based method to estimate the time-varying regression function and provide asymptotic theory for our estimates. Moreover, we show that the main conditions of the theory are satis ed for a large class of nonlinear autoregressive processes with a time-varying regression function. Finally, we examine structured models where the regression function splits up into time-varying additive components. As will be seen, estimation in these models does not su er from the curse of dimensionality. We complement the technical analysis of the paper by an application to nancial data.

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    File URL: http://www.cemmap.ac.uk/wps/cwp221212.pdf
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    Bibliographic Info

    Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP22/12.

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    Date of creation: Sep 2012
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    Handle: RePEc:ifs:cemmap:22/12

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    Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE
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    Related research

    Keywords: local stationarity; nonparametric regression; smooth backfitting;

    This paper has been announced in the following NEP Reports:

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    1. Martens, Martin & van Dijk, Dick, 2007. "Measuring volatility with the realized range," Journal of Econometrics, Elsevier, vol. 138(1), pages 181-207, May.
    2. Kristensen, Dennis, 2009. "Uniform Convergence Rates Of Kernel Estimators With Heterogeneous Dependent Data," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1433-1445, October.
    3. R. Dahlhaus & M. Neumann & R. von Sachs, 1997. "Nonlinear Wavelet Estimation of Time-Varying Autoregressive Processes," SFB 373 Discussion Papers 1997,34, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Oliver Linton & E. Mammen & J. Nielsen, 1999. "The existence and asymptotic properties of a backfitting projection algorithm under weak conditions," LSE Research Online Documents on Economics 300, London School of Economics and Political Science, LSE Library.
    5. Bhattacharya, Rabi & Lee, Chanho, 1995. "On geometric ergodicity of nonlinear autoregressive models," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 311-315, March.
    6. Christian M. Hafner & Oliver Linton, 2009. "Efficient Estimation of a Multivariate Multiplicative Volatility Model," STICERD - Econometrics Paper Series /2009/541, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. repec:wop:humbsf:1997-34 is not listed on IDEAS
    8. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    9. Yang, Dennis & Zhang, Qiang, 2000. "Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices," The Journal of Business, University of Chicago Press, vol. 73(3), pages 477-91, July.
    10. Wu, Guojun & Xiao, Zhijie, 2002. "A generalized partially linear model of asymmetric volatility," Journal of Empirical Finance, Elsevier, vol. 9(3), pages 287-319, August.
    11. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(03), pages 726-748, June.
    12. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range-Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, 06.
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