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A general asymptotic theory for time‐series models

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  • Shiqing Ling
  • Michael McAleer

Abstract

This paper develops a general asymptotic theory for the estimation of strictly stationary and ergodic time–series models. Under simple conditions that are straightforward to check, we establish the strong consistency, the rate of strong convergence and the asymptotic normality of a general class of estimators that includes LSE, MLE and some M‐type estimators. As an application, we verify the assumptions for the long‐memory fractional ARIMA model. Other examples include the GARCH(1,1) model, random coefficient AR(1) model and the threshold MA(1) model.

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  • Shiqing Ling & Michael McAleer, 2010. "A general asymptotic theory for time‐series models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 97-111, February.
    • Handle: RePEc:bla:stanee:v:64:y:2010:i:1:p:97-111
    DOI: 10.1111/j.1467-9574.2009.00447.x
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    References listed on IDEAS

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    1. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    2. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606, November.
    3. Ling S., 2003. "Adaptive Estimators and Tests of Stationary and Nonstationary Short- and Long-Memory ARFIMA-GARCH Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 955-967, January.
    4. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    5. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    6. Shiqing Ling, 2004. "Estimation and testing stationarity for double‐autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 63-78, February.
    7. J. Pfanzagl, 1969. "On the measurability and consistency of minimum contrast estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 14(1), pages 249-272, December.
    8. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590, November.
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    Cited by:

    1. Chang, C-L. & Hsu, S.-H. & McAleer, M.J., 2018. "Asymmetric Risk Impacts of Chinese Tourists to Taiwan," Econometric Institute Research Papers EI2018-18, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Song, Junmo & Oh, Dong-hyun & Kang, Jiwon, 2017. "Robust estimation in stochastic frontier models," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 243-267.
    3. Mawuli Segnon, 2022. "Strict stationarity of Poisson integer-valued ARCH processes of order infinity," CQE Working Papers 10222, Center for Quantitative Economics (CQE), University of Muenster.
    4. Davide Delle Monache & Stefano Grassi & Paolo Santucci de Magistris, 2017. "Does the ARFIMA really shift?," CREATES Research Papers 2017-16, Department of Economics and Business Economics, Aarhus University.
    5. Caporin, Massimiliano & Rossi, Eduardo & Santucci de Magistris, Paolo, 2017. "Chasing volatility," Journal of Econometrics, Elsevier, vol. 198(1), pages 122-145.
    6. Poloni, Federico & Sbrana, Giacomo, 2015. "A note on forecasting demand using the multivariate exponential smoothing framework," International Journal of Production Economics, Elsevier, vol. 162(C), pages 143-150.
    7. Ke Zhu & Shiqing Ling, 2015. "LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 784-794, June.
    8. Poloni, Federico & Sbrana, Giacomo, 2019. "Closed-form results for vector moving average models with a univariate estimation approach," Econometrics and Statistics, Elsevier, vol. 10(C), pages 27-52.
    9. Christian Francq & Jean-Michel Zakoïan, 2013. "Estimating the Marginal Law of a Time Series With Applications to Heavy-Tailed Distributions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 412-425, October.

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