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Asymptotic Theory On The Least Squares Estimation Of Threshold Moving-Average Models

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  • Li, Dong
  • Ling, Shiqing
  • Li, Wai Keung

Abstract

This paper studies the asymptotic theory of least squares estimation in a threshold moving average model. Under some mild conditions, it is shown that the estimator of the threshold is n-consistent and its limiting distribution is related to a two-sided compound Poisson process, whereas the estimators of other coefficients are strongly consistent and asymptotically normal. This paper also provides a resampling method to tabulate the limiting distribution of the estimated threshold in practice, which is the first successful effort in this direction. This resampling method contributes to threshold literature. Simultaneously, simulation studies are carried out to assess the performance of least squares estimation in finite samples.

Suggested Citation

  • Li, Dong & Ling, Shiqing & Li, Wai Keung, 2013. "Asymptotic Theory On The Least Squares Estimation Of Threshold Moving-Average Models," Econometric Theory, Cambridge University Press, vol. 29(3), pages 482-516, June.
    • Handle: RePEc:cup:etheor:v:29:y:2013:i:03:p:482-516_00
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    Cited by:

    1. Wu, K.Y.K. & Li, W.K., 2015. "Double Generalized Threshold Models with constraint on the dispersion by the mean," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 59-73.
    2. Li, Dong & Ling, Shiqing & Zakoïan, Jean-Michel, 2015. "Asymptotic inference in multiple-threshold double autoregressive models," Journal of Econometrics, Elsevier, vol. 189(2), pages 415-427.
    3. Chih‐Hao Chang & Kam‐Fai Wong & Wei‐Yee Lim, 2023. "Threshold estimation for continuous three‐phase polynomial regression models with constant mean in the middle regime," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(1), pages 4-47, February.
    4. Ke Zhu & Wai Keung Li & Philip L. H. Yu, 2017. "Buffered Autoregressive Models With Conditional Heteroscedasticity: An Application to Exchange Rates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 528-542, October.
    5. Dong Li & Shiqing Ling & Jean-Michel Zakoian, 2013. "Asymptotic Inference in Multiple-Threshold Nonlinear Time Series Models," Working Papers 2013-51, Center for Research in Economics and Statistics.
    6. Yang, Yaxing & Ling, Shiqing, 2017. "Self-weighted LAD-based inference for heavy-tailed threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 197(2), pages 368-381.
    7. Zhang, Xinyu & Li, Dong & Tong, Howell, 2023. "On the least squares estimation of multiple-threshold-variable autoregressive models," LSE Research Online Documents on Economics 118377, London School of Economics and Political Science, LSE Library.

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