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Non-parametric regression with a latent time series

  • Oliver Linton
  • Jens Perch Nielsen
  • Søren Feodor Nielsen

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

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Article provided by Royal Economic Society in its journal Econometrics Journal.

Volume (Year): 12 (2009)
Issue (Month): 2 (07)
Pages: 187-207

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Handle: RePEc:ect:emjrnl:v:12:y:2009:i:2:p:187-207
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  1. Jushan Bai & Serena Ng, 2000. "Determining the Number of Factors in Approximate Factor Models," Econometric Society World Congress 2000 Contributed Papers 1504, Econometric Society.
  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.
  3. 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.
  4. M. Hashem Pesaran, 2004. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," CESifo Working Paper Series 1331, CESifo Group Munich.
  5. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
  6. Bent Nielsen & Lars Hougaard Hansen, 2004. "Two sided analysis of variance with a latent time series," Economics Series Working Papers 2004-W25, University of Oxford, Department of Economics.
  7. Steve Berry & Oliver Linton & Ariel Pakes, 2000. "Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems," STICERD - Econometrics Paper Series 400, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  8. 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.
  9. Bai, Jushan, 2004. "Estimating cross-section common stochastic trends in nonstationary panel data," Journal of Econometrics, Elsevier, vol. 122(1), pages 137-183, September.
  10. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291, March.
  11. Lars Hougaard Hansen & Bent Nielsen & Jens Perch Nielsen, 2004. "Two sided analysis of variance with a latent time series," Economics Papers 2004-W25, Economics Group, Nuffield College, University of Oxford.
  12. Ekaterini Kyriazidou, 1997. "Estimation of a Panel Data Sample Selection Model," Econometrica, Econometric Society, vol. 65(6), pages 1335-1364, November.
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