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Second-Order Least Squares Estimation in Nonlinear Time Series Models with ARCH Errors

Author

Listed:
  • Mustafa Salamh

    (Department of Statistics, Cairo University, Giza 12613, Egypt)

  • Liqun Wang

    (Department of Statistics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada)

Abstract

Many financial and economic time series exhibit nonlinear patterns or relationships. However, most statistical methods for time series analysis are developed for mean-stationary processes that require transformation, such as differencing of the data. In this paper, we study a dynamic regression model with nonlinear, time-varying mean function, and autoregressive conditionally heteroscedastic errors. We propose an estimation approach based on the first two conditional moments of the response variable, which does not require specification of error distribution. Strong consistency and asymptotic normality of the proposed estimator is established under strong-mixing condition, so that the results apply to both stationary and mean-nonstationary processes. Moreover, the proposed approach is shown to be superior to the commonly used quasi-likelihood approach and the efficiency gain is significant when the (conditional) error distribution is asymmetric. We demonstrate through a real data example that the proposed method can identify a more accurate model than the quasi-likelihood method.

Suggested Citation

  • Mustafa Salamh & Liqun Wang, 2021. "Second-Order Least Squares Estimation in Nonlinear Time Series Models with ARCH Errors," Econometrics, MDPI, vol. 9(4), pages 1-17, November.
  • Handle: RePEc:gam:jecnmx:v:9:y:2021:i:4:p:41-:d:689472
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    References listed on IDEAS

    as
    1. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, September.
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    5. Mustafa Salamh & Liqun Wang, 2021. "Second-Order Least Squares Method for Dynamic Panel Data Models with Application," JRFM, MDPI, vol. 14(9), pages 1-19, September.
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    Cited by:

    1. Alexander Mayer, 2022. "Two-step estimation in linear regressions with adaptive learning," Papers 2204.05298, arXiv.org, revised Nov 2022.

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