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Sieve inference on possibly misspecified semi-nonparametric time series models

Author

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  • Chen, Xiaohong
  • Liao, Zhipeng
  • Sun, Yixiao

Abstract

This paper establishes the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi-nonparametric time series models. We show that, even when the sieve score process is not a martingale difference sequence, the asymptotic variance in the case of irregular functionals is the same as those for independent data. Using an orthonormal series long run variance estimator, we construct a “pre-asymptotic” Wald statistic and show that it is asymptotically F distributed. Simulations indicate that our “pre-asymptotic” Wald test with F critical values has more accurate size in finite samples than the conventional Wald test with chi-square critical values.

Suggested Citation

  • Chen, Xiaohong & Liao, Zhipeng & Sun, Yixiao, 2014. "Sieve inference on possibly misspecified semi-nonparametric time series models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 639-658.
  • Handle: RePEc:eee:econom:v:178:y:2014:i:p3:p:639-658
    DOI: 10.1016/j.jeconom.2013.10.002
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    References listed on IDEAS

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    1. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(01), pages 116-142, February.
    2. Yixiao Sun, 2013. "A heteroskedasticity and autocorrelation robust F test using an orthonormal series variance estimator," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 1-26, February.
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    10. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    11. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76 Elsevier.
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    Citations

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    Cited by:

    1. Chen, Xiaohong & Liao, Zhipeng, 2014. "Sieve M inference on irregular parameters," Journal of Econometrics, Elsevier, vol. 182(1), pages 70-86.
    2. Byunghoon Kang, 2017. "Inference in Nonparametric Series Estimation with Data-Dependent Undersmoothing," Working Papers 170712442, Lancaster University Management School, Economics Department.
    3. Kim, Min Seong & Sun, Yixiao & Yang, Jingjing, 2017. "A fixed-bandwidth view of the pre-asymptotic inference for kernel smoothing with time series data," Journal of Econometrics, Elsevier, vol. 197(2), pages 298-322.
    4. Sun, Yixiao, 2013. "Fixed-smoothing Asymptotics in a Two-step GMM Framework," University of California at San Diego, Economics Working Paper Series qt64x4z265, Department of Economics, UC San Diego.
    5. Timothy Christensen, 2014. "Nonparametric Stochastic Discount Factor Decomposition," Papers 1412.4428, arXiv.org, revised May 2017.
    6. Chen, Xiaohong & Liao, Zhipeng, 2015. "Sieve semiparametric two-step GMM under weak dependence," Journal of Econometrics, Elsevier, vol. 189(1), pages 163-186.
    7. Adrian, Tobias & Boyarchenko, Nina & Giannone, Domenico, 2016. "Vulnerable Growth," CEPR Discussion Papers 11583, C.E.P.R. Discussion Papers.
    8. Chen, Xiaohong & Christensen, Timothy M., 2015. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," Journal of Econometrics, Elsevier, vol. 188(2), pages 447-465.
    9. Adrian, Tobias & Crump, Richard K. & Vogt, Erik, 2015. "Nonlinearity and flight to safety in the risk-return trade-off for stocks and bonds," Staff Reports 723, Federal Reserve Bank of New York, revised 01 Nov 2017.
    10. Bartalotti, Otávio, 2018. "Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation," IZA Discussion Papers 11560, Institute for the Study of Labor (IZA).
    11. Giovanni Compiani & Philip A. Haile & Marcelo Sant'Anna, 2018. "Common Values, Unobserved Heterogeneity, and Endogenous Entry in U.S. Offshore Oil Lease Auctions," Cowles Foundation Discussion Papers 2137, Cowles Foundation for Research in Economics, Yale University.
    12. Bruno Merlevede & Angelos Theodorakopoulos, 2016. "Productivity effects from inter-industry offshoring and inshoring: Firm-level evidence from Belgium," FIW Working Paper series 165, FIW.
    13. repec:taf:jnlbes:v:35:y:2017:i:3:p:371-388 is not listed on IDEAS
    14. Vogt, Erik, 2014. "Option-implied term structures," Staff Reports 706, Federal Reserve Bank of New York, revised 01 Jan 2016.
    15. James Wolter, 2015. "Asymptotics for Sieve Estimators of Hazard Rates: Estimating Hazard Functionals," Economics Series Working Papers 760, University of Oxford, Department of Economics.
    16. Timothy M. Christensen, 2015. "Nonparametric stochastic discount factor decomposition," CeMMAP working papers CWP24/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    Keywords

    Sieve M estimation; Sieve Riesz representer; Irregular functional; Pre-asymptotic variance; Orthonormal series long run variance estimation; F distribution;

    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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