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Sieve inference on semi-nonparametric time series models

Author

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  • Xiaohong Chen

    (Institute for Fiscal Studies and Yale University)

  • . .

    (Institute for Fiscal Studies)

  • Yixiao Sun

    (Institute for Fiscal Studies)

Abstract

The method of sieves has been widely used in estimating semiparametric and nonparametric models. In this paper, we first provide a general theory on the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi/nonparametric time series models. Next, we establish a surprising result that the asymptotic variances of plug-in sieve M estimators of irregular (i.e., slower than root-T estimable) functionals do not depend on temporal dependence. Nevertheless, ignoring the temporal dependence in small samples may not lead to accurate inference. We then propose an easy-to-compute and more accurate inference procedure based on a "pre-asymptotic" sieve variance estimator that captures temporal dependence. We construct a "pre-asymptotic" Wald statistic using an orthonormal series long run variance (OS-LRV) estimator. For sieve M estimators of both regular (i.e., root-T estimable) and irregular functionals, a scaled "pre-asymptotic" Wald statistic is asymptotically F distributed when the series number of terms in the OS-LRV estimator is held fixed. Simulations indicate that our scaled "pre-asymptotic" Wald test with F critical values has more accurate size in finite samples than the usual Wald test with chi-square critical values.

Suggested Citation

  • Xiaohong Chen & . . & Yixiao Sun, 2012. "Sieve inference on semi-nonparametric time series models," CeMMAP working papers CWP06/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:06/12
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    References listed on IDEAS

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    Cited by:

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    2. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn & Zhipeng Liao, 2014. "Asymptotic Efficiency of Semiparametric Two-step GMM," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(3), pages 919-943.
    3. Lee, Jungyoon & Robinson, Peter M., 2016. "Series estimation under cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 190(1), pages 1-17.
    4. Jungyoon Lee & Peter Robinson, 2016. "Series estimation under cross-sectional dependence," LSE Research Online Documents on Economics 63380, London School of Economics and Political Science, LSE Library.
    5. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Quasi Likelihood Ratio Inference on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897, Cowles Foundation for Research in Economics, Yale University.
    6. Peter C.B. Phillips & Zhipeng Liao, 2012. "Series Estimation of Stochastic Processes: Recent Developments and Econometric Applications," Cowles Foundation Discussion Papers 1871, Cowles Foundation for Research in Economics, Yale University.
    7. Yining Chen, 2015. "Semiparametric Time Series Models with Log-concave Innovations: Maximum Likelihood Estimation and its Consistency," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 1-31, March.

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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