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Nonparametric Estimation Of Additive Nonlinear Arx Time Series: Local Linear Fitting And Projections

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  • Cai, Zongwu
  • Masry, Elias

Abstract

We consider the estimation and identification of the components (endogenous and exogenous) of additive nonlinear ARX time series models. We employ a local polynomial fitting scheme coupled with projections. We establish the weak consistency (with rates) and the asymptotic normality of the projection estimates of the additive components. Expressions for the asymptotic bias and variance are given.

Suggested Citation

  • Cai, Zongwu & Masry, Elias, 2000. "Nonparametric Estimation Of Additive Nonlinear Arx Time Series: Local Linear Fitting And Projections," Econometric Theory, Cambridge University Press, vol. 16(4), pages 465-501, August.
    • Handle: RePEc:cup:etheor:v:16:y:2000:i:04:p:465-501_16
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    Cited by:

    1. Hossein Hassani & Mohammad Reza Yeganegi & Rangan Gupta, 2019. "Does inequality really matter in forecasting real housing returns of the United Kingdom?," International Economics, CEPII research center, issue 159, pages 18-25.
    2. Zongwu Cai & Xiyuan Liu, 2020. "A Functional-Coefficient VAR Model for Dynamic Quantiles with Constructing Financial Network," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202017, University of Kansas, Department of Economics, revised Oct 2020.
    3. Hossein Hassani & Mohammad Reza Yeganegi & Rangan Gupta & Riza Demirer, 2018. "Forecasting Stock Market (Realized) Volatility in the United Kingdom: Is There a Role for Economic Inequality?," Working Papers 201880, University of Pretoria, Department of Economics.
    4. Ying Wang & Peter C. B. Phillips & Yundong Tu, 2024. "Limit Theory and Inference in Non-cointegrated Functional Coefficient Regression," Cowles Foundation Discussion Papers 2399, Cowles Foundation for Research in Economics, Yale University.
    5. Zhou, Xing-cai & Xu, Ying-zhi & Lin, Jin-guan, 2017. "Wavelet estimation in varying coefficient models for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 179-189.
    6. Zongwu Cai & Ying Fang & Dingshi Tian, 2018. "Assessing Tail Risk Using Expectile Regressions with Partially Varying Coefficients," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201804, University of Kansas, Department of Economics, revised Oct 2018.
    7. Kim, Woocheol & Linton, Oliver, 2003. "A local instrumental variable estimation method for generalized additive volatility models," LSE Research Online Documents on Economics 2028, London School of Economics and Political Science, LSE Library.
    8. Zongwu Cai & Xiyuan Liu, 2020. "A Nonparametric Dynamic Network via Multivariate Quantile Autoregressions," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202209, University of Kansas, Department of Economics, revised Mar 2022.
    9. Hossein Hassani & Mohammad Reza Yeganegi & Rangan Gupta & Riza Demirer, 2022. "Forecasting stock market (realized) volatility in the United Kingdom: Is there a role of inequality?," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(2), pages 2146-2152, April.
    10. repec:wyi:journl:002114 is not listed on IDEAS
    11. 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.
    12. Zongwu Cai & Gunawan, 2023. "A Combination Forecast for Nonparametric Models with Structural Breaks," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202310, University of Kansas, Department of Economics, revised Sep 2023.
    13. Peter Martey Addo, 2014. "Multivariate Self-Exciting Threshold Autoregressive Models with eXogenous Input," Papers 1407.7738, arXiv.org.
    14. Cai, Zongwu & Xiao, Zhijie, 2012. "Semiparametric quantile regression estimation in dynamic models with partially varying coefficients," Journal of Econometrics, Elsevier, vol. 167(2), pages 413-425.
    15. Cai, Zongwu & Chen, Linna & Fang, Ying, 2018. "A semiparametric quantile panel data model with an application to estimating the growth effect of FDI," Journal of Econometrics, Elsevier, vol. 206(2), pages 531-553.

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