IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2009cf670.html
   My bibliography  Save this paper

A General Asymptotic Theory for Time Series Models

Author

Listed:
  • Shiqing Ling

    (Department of Mathematics, Hong Kong University of Science and Technology)

  • Michael McAleer

    (Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam and Tinbergen Institute and Center for International Research on the Japanese Economy (CIRJE), Faculty of Economics, University of Tokyo)

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.

Suggested Citation

  • Shiqing Ling & Michael McAleer, 2009. "A General Asymptotic Theory for Time Series Models," CIRJE F-Series CIRJE-F-670, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2009cf670
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2009/2009cf670.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    3. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    4. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590.
    5. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    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. 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.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Caporin, Massimiliano & Rossi, Eduardo & Santucci de Magistris, Paolo, 2017. "Chasing volatility," Journal of Econometrics, Elsevier, vol. 198(1), pages 122-145.
    6. 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.
    7. 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.
    8. 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.
    9. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pierre Perron & Zhongjun Qu, 2007. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts," Boston University - Department of Economics - Working Papers Series wp2007-044, Boston University - Department of Economics.
    2. Karim M. Abadir & Gabriel Talmain, 2012. "Beyond Co-Integration: Modelling Co-Movements in Macro finance," Working Paper series 25_12, Rimini Centre for Economic Analysis.
    3. Kyaw, NyoNyo A. & Los, Cornelis A. & Zong, Sijing, 2006. "Persistence characteristics of Latin American financial markets," Journal of Multinational Financial Management, Elsevier, vol. 16(3), pages 269-290, July.
    4. Perron, Pierre & Qu, Zhongjun, 2010. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 275-290.
    5. Renzo Pardo Figueroa & Gabriel Rodríguez, 2014. "Distinguishing between True and Spurious Long Memory in the Volatility of Stock Market Returns in Latin America," Documentos de Trabajo / Working Papers 2014-395, Departamento de Economía - Pontificia Universidad Católica del Perú.
    6. Pierre Perron & Zhongjun Qu, 2006. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts and its Implications for Stock Returns Volatility," Boston University - Department of Economics - Working Papers Series WP2006-016, Boston University - Department of Economics.
    7. Kramer, Walter & Hassler, Uwe, 1998. "Limiting efficiency of OLS vs. GLS when regressors are fractionally integrated," Economics Letters, Elsevier, vol. 60(3), pages 285-290, September.
    8. Andrés Herrera Aramburú & Gabriel Rodríguez, 2016. "Volatility of stock market and exchange rate returns in Peru: Long memory or short memory with level shifts?," International Journal of Monetary Economics and Finance, Inderscience Enterprises Ltd, vol. 9(1), pages 45-66.
    9. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    10. Bent Jesper Christensen & Morten Ørregaard Nielsen, 2007. "The Effect of Long Memory in Volatility on Stock Market Fluctuations," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 684-700, November.
    11. Lu, Yang K. & Perron, Pierre, 2010. "Modeling and forecasting stock return volatility using a random level shift model," Journal of Empirical Finance, Elsevier, vol. 17(1), pages 138-156, January.
    12. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911.
    13. Gabriel Rodríguez, 2016. "Modeling Latin-American Stock and Forex Markets Volatility: Empirical Application of a Model with Random Level Shifts and Genuine Long Memory [Modelando la volatilidad de los mercados bursátiles y cam," Documentos de Trabajo / Working Papers 2016-416, Departamento de Economía - Pontificia Universidad Católica del Perú.
    14. Gabriel Rodríguez & José Carlos Gonzáles Tanaka, 2016. "An Empirical Application of a Random Level Shifts Model with Time-Varying Probability and Mean Reversion to the Volatility of Latin-American Forex Markets Returns [Una aplicación empírica de un modelo," Documentos de Trabajo / Working Papers 2016-415, Departamento de Economía - Pontificia Universidad Católica del Perú.
    15. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
    16. Christensen, Bent Jesper & Nielsen, Morten Orregaard, 2006. "Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting," Journal of Econometrics, Elsevier, vol. 133(1), pages 343-371, July.
    17. Rodríguez, Gabriel, 2017. "Modeling Latin-American stock and Forex markets volatility: Empirical application of a model with random level shifts and genuine long memory," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 393-420.
    18. Lieberman, Offer & Phillips, Peter C.B., 2008. "A complete asymptotic series for the autocovariance function of a long memory process," Journal of Econometrics, Elsevier, vol. 147(1), pages 99-103, November.
    19. repec:ebl:ecbull:v:3:y:2007:i:16:p:1-14 is not listed on IDEAS
    20. Ling, Shiqing, 2007. "Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models," Journal of Econometrics, Elsevier, vol. 140(2), pages 849-873, October.
    21. Evans, Kevin P. & Speight, Alan E.H., 2010. "Intraday periodicity, calendar and announcement effects in Euro exchange rate volatility," Research in International Business and Finance, Elsevier, vol. 24(1), pages 82-101, January.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tky:fseres:2009cf670. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CIRJE administrative office (email available below). General contact details of provider: https://edirc.repec.org/data/ritokjp.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.