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Penalized Sieve Estimation and Inference of Semi-Nonparametric Dynamic Models: A Selective Review

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Abstract

In this selective review, we first provide some empirical examples that motivate the usefulness of semi-nonparametric techniques in modelling economic and financial time series. We describe popular classes of semi-nonparametric dynamic models and some temporal dependence properties. We then present penalized sieve extremum (PSE) estimation as a general method for semi-nonparametric models with cross-sectional, panel, time series, or spatial data. The method is especially powerful in estimating difficult ill-posed inverse problems such as semi-nonparametric mixtures or conditional moment restrictions. We review recent advances on inference and large sample properties of the PSE estimators, which include (1) consistency and convergence rates of the PSE estimator of the nonparametric part; (2) limiting distributions of plug-in PSE estimators of functionals that are either smooth (i.e., root-n estimable) or non-smooth (i.e., slower than root-n estimable); (3) simple criterion-based inference for plug-in PSE estimation of smooth or non-smooth functionals; and (4) root-n asymptotic normality of semiparametric two-step estimators and their consistent variance estimators. Examples from dynamic asset pricing, nonlinear spatial VAR, semiparametric GARCH, and copula-based multivariate financial models are used to illustrate the general results.

Suggested Citation

  • Xiaohong Chen, 2011. "Penalized Sieve Estimation and Inference of Semi-Nonparametric Dynamic Models: A Selective Review," Cowles Foundation Discussion Papers 1804, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1804
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d18/d1804.pdf
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    1. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    2. de Jong, Robert M., 2002. "A note on "Convergence rates and asymptotic normality for series estimators": uniform convergence rates," Journal of Econometrics, Elsevier, vol. 111(1), pages 1-9, November.
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    Keywords

    Nonlinear time series; Temporal dependence; Tail dependence; Penalized sieve M estimation; Penalized sieve minimum distance; Semiparametric two-step; Nonlinear ill-posed inverse; Mixtures; Conditional moment restrictions; Nonparametric endogeneity; Dynamic asset pricing; Varying coefficient VAR; GARCH; Copulas; Value-at-risk;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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