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Non-parametric regression with a latent time series

Author

Listed:
  • Oliver Linton
  • Jens Perch Nielsen
  • Søren Feodor Nielsen

Abstract

In this paper we investigate a class of semi-parametric models for panel data sets where the cross-section and time dimensions are large. Our model contains a latent time series that is to be estimated and perhaps forecasted along with a non-parametric covariate effect. Our model is motivated by the need to be flexible with regard to the functional form of covariate effects but also the need to be practical with regard to forecasting of time series effects. We propose estimation procedures based on local linear kernel smoothing; our estimators are all explicitly given. We establish the pointwise consistency and asymptotic normality of our estimators. We also show that the effects of estimating the latent time series can be ignored in certain cases. Copyright © 2009 The Author(s). Journal compilation © Royal Economic Society 2009

Suggested Citation

  • Oliver Linton & Jens Perch Nielsen & Søren Feodor Nielsen, 2009. "Non-parametric regression with a latent time series," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 187-207, July.
    • Handle: RePEc:ect:emjrnl:v:12:y:2009:i:2:p:187-207
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    References listed on IDEAS

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    1. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    2. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
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    4. Matthias R. Fengler & Wolfgang K. Härdle & Enno Mammen, 0. "A semiparametric factor model for implied volatility surface dynamics," Journal of Financial Econometrics, Oxford University Press, vol. 5(2), pages 189-218.
    5. Steve Berry & Oliver B. Linton & Ariel Pakes, 2004. "Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 613-654.
    6. Fan, Jianqing & Huang, Tao & Li, Runze, 2007. "Analysis of Longitudinal Data With Semiparametric Estimation of Covariance Function," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 632-641, June.
    7. Bai, Jushan, 2004. "Estimating cross-section common stochastic trends in nonstationary panel data," Journal of Econometrics, Elsevier, vol. 122(1), pages 137-183, September.
    8. Ekaterini Kyriazidou, 1997. "Estimation of a Panel Data Sample Selection Model," Econometrica, Econometric Society, vol. 65(6), pages 1335-1364, November.
    9. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    10. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    11. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
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    2. Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 99-110, January.
    3. Lena Boneva (Körber) & Oliver Linton & Michael Vogt, 2013. "A semiparametric model for heterogeneous panel data with fixed effects," CeMMAP working papers 02/13, Institute for Fiscal Studies.
    4. Dursun Aydın & Ersin Yılmaz, 2021. "Semiparametric modeling of the right-censored time-series based on different censorship solution techniques," Empirical Economics, Springer, vol. 61(4), pages 2143-2172, October.
    5. Boneva, Lena & Linton, Oliver & Vogt, Michael, 2015. "A semiparametric model for heterogeneous panel data with fixed effects," Journal of Econometrics, Elsevier, vol. 188(2), pages 327-345.
    6. Mammen, Enno & Park, Byeong U. & Schienle, Melanie, 2012. "Additive models: Extensions and related models," SFB 649 Discussion Papers 2012-045, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.

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