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Local Polynomial Estimation of Time-Varying Parameters in Nonlinear Models

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  • Dennis Kristensen
  • Young Jun Lee

Abstract

We develop a novel asymptotic theory for local polynomial (quasi-) maximum-likelihood estimators of time-varying parameters in a broad class of nonlinear time series models. Under weak regularity conditions, we show the proposed estimators are consistent and follow normal distributions in large samples. Our conditions impose weaker smoothness and moment conditions on the data-generating process and its likelihood compared to existing theories. Furthermore, the bias terms of the estimators take a simpler form. We demonstrate the usefulness of our general results by applying our theory to local (quasi-)maximum-likelihood estimators of a time-varying VAR's, ARCH and GARCH, and Poisson autogressions. For the first three models, we are able to substantially weaken the conditions found in the existing literature. For the Poisson autogression, existing theories cannot be be applied while our novel approach allows us to analyze it.

Suggested Citation

  • Dennis Kristensen & Young Jun Lee, 2019. "Local Polynomial Estimation of Time-Varying Parameters in Nonlinear Models," Papers 1904.05209, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:1904.05209
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    References listed on IDEAS

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    1. Agosto, Arianna & Cavaliere, Giuseppe & Kristensen, Dennis & Rahbek, Anders, 2016. "Modeling corporate defaults: Poisson autoregressions with exogenous covariates (PARX)," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 640-663.
    2. Heejoon Han & Dennis Kristensen, 2014. "Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 416-429, July.
    3. Dennis Kristensen, 2012. "Non‐parametric detection and estimation of structural change," Econometrics Journal, Royal Economic Society, vol. 15(3), pages 420-461, October.
    4. Fryzlewicz, Piotr & Sapatinas, Theofanis & Subba Rao, Suhasini, 2008. "Normalized least-squares estimation in time-varying ARCH models," LSE Research Online Documents on Economics 25187, London School of Economics and Political Science, LSE Library.
    5. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
    6. Chen, Bin & Hong, Yongmiao, 2016. "Detecting For Smooth Structural Changes In Garch Models," Econometric Theory, Cambridge University Press, vol. 32(3), pages 740-791, June.
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    Cited by:

    1. David T. Frazier & Bonsoo Koo, 2020. "Indirect Inference for Locally Stationary Models," Monash Econometrics and Business Statistics Working Papers 30/20, Monash University, Department of Econometrics and Business Statistics.
    2. Frazier, David T. & Koo, Bonsoo, 2021. "Indirect inference for locally stationary models," Journal of Econometrics, Elsevier, vol. 223(1), pages 1-27.

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