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A Fixed-bandwidth View of the Pre-asymptotic Inference for Kernel Smoothing with Time Series Data

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  • Kim, Min Seong
  • Sun, Yixiao
  • Yang, Jingjing

Abstract

This paper develops robust testing procedures for nonparametric kernel methods in the presence of temporal dependence of unknown forms. Based on the fixed-bandwidth asymptotic variance and the pre-asymptotic variance, we propose a heteroskedasticity and autocorrelation robust (HAR) variance estimator that achieves double robustness --- it is asymptotically valid regardless of whether the temporal dependence is present or not, and whether the kernel smoothing bandwidth is held constant or allowed to decay with the sample size. Using the HAR variance estimator, we construct the studentized test statistic and examine its asymptotic properties under both the fixed-smoothing and increasing-smoothing asymptotics. The fixed-smoothing approximation and the associated convenient t-approximation achieve extra robustness --- it is asymptotically valid regardless of whether the truncation lag parameter governing the covariance weighting grows at the same rate as or a slower rate than the sample size. Finally, we suggest a simulation-based calibration approach to choose smoothing parameters that optimize testing oriented criteria. Simulation shows that the proposed procedures work very well in finite samples.

Suggested Citation

  • Kim, Min Seong & Sun, Yixiao & Yang, Jingjing, 2016. "A Fixed-bandwidth View of the Pre-asymptotic Inference for Kernel Smoothing with Time Series Data," University of California at San Diego, Economics Working Paper Series qt2240n3n5, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt2240n3n5
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    References listed on IDEAS

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    Cited by:

    1. Bartalotti Otávio, 2019. "Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-26, January.
    2. Hwang, Jungbin & Sun, Yixiao, 2018. "Should we go one step further? An accurate comparison of one-step and two-step procedures in a generalized method of moments framework," Journal of Econometrics, Elsevier, vol. 207(2), pages 381-405.

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    More about this item

    Keywords

    Social and Behavioral Sciences; heteroskedasticity and autocorrelation robust variance; calibration; fixed-smoothing asymptotics; fixed-bandwidth asymptotics; kernel density estimator; local polynomial estimator; t-approximation; testing-optimal smoothing-parameters choice; temporal dependence;
    All these keywords.

    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
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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