IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v123y2014i3p305-307.html
   My bibliography  Save this article

On conditions in central limit theorems for martingale difference arrays

Author

Listed:
  • Alj, Abdelkamel
  • Azrak, Rajae
  • Mélard, Guy

Abstract

An alternative central limit theorem for martingale difference arrays is presented. It can be deduced from the literature but it is not stated as such. It can be very useful for statisticians and econometricians. An illustration is given in the context of ARMA models with time-dependent coefficients. This note ends with a discussion about the conditions.

Suggested Citation

  • Alj, Abdelkamel & Azrak, Rajae & Mélard, Guy, 2014. "On conditions in central limit theorems for martingale difference arrays," Economics Letters, Elsevier, vol. 123(3), pages 305-307.
    • Handle: RePEc:eee:ecolet:v:123:y:2014:i:3:p:305-307
    DOI: 10.1016/j.econlet.2014.03.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176514000998
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2014.03.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Rajae Azrak & Guy Mélard, 2006. "Asymptotic Properties of Quasi-Maximum Likelihood Estimators for ARMA Models with Time-Dependent Coefficients," Statistical Inference for Stochastic Processes, Springer, vol. 9(3), pages 279-330, October.
    2. Rajae Azrak & Guy Melard, 2006. "Asymptotic properties of quasi-maximum likelihood estimators for ARMA models with time-dependent coefficients," ULB Institutional Repository 2013/13758, ULB -- Universite Libre de Bruxelles.
    3. Abdelkamel Alj & Rajae Azrak & Guy Melard, 2014. "On Conditions in Central Limit Theorems for Martingale Difference Arrays Long Version," Working Papers ECARES ECARES 2014-05, ULB -- Universite Libre de Bruxelles.
    4. Richard A. Davis & William T. M. Dunsmuir & Sarah B. Streett, 2005. "Maximum Likelihood Estimation for an Observation Driven Model for Poisson Counts," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 149-159, June.
    5. Onatski, Alexei, 2012. "Asymptotics of the principal components estimator of large factor models with weakly influential factors," Journal of Econometrics, Elsevier, vol. 168(2), pages 244-258.
    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. Blöchlinger, Andreas, 2021. "Interest rate risk in the banking book: A closed-form solution for non-maturity deposits," Journal of Banking & Finance, Elsevier, vol. 125(C).
    2. Chakraborty, Saptarshi & Bhattacharya, Suman K. & Khare, Kshitij, 2022. "Estimating accuracy of the MCMC variance estimator: Asymptotic normality for batch means estimators," Statistics & Probability Letters, Elsevier, vol. 183(C).
    3. Rajae Azrak & Guy Mélard, 2022. "Autoregressive Models with Time-Dependent Coefficients—A Comparison between Several Approaches," Stats, MDPI, vol. 5(3), pages 1-21, August.
    4. Rajae Azrak & Guy Mélard, 2021. "Asymptotic properties of conditional least-squares estimators for array time series," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 525-547, October.

    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. Abdelkamel Alj & Rajae Azrak & Guy Melard, 2014. "On Conditions in Central Limit Theorems for Martingale Difference Arrays Long Version," Working Papers ECARES ECARES 2014-05, ULB -- Universite Libre de Bruxelles.
    2. Rajae Azrak & Guy Mélard, 2022. "Autoregressive Models with Time-Dependent Coefficients—A Comparison between Several Approaches," Stats, MDPI, vol. 5(3), pages 1-21, August.
    3. Rajae Azrak & Guy Mélard, 2021. "Asymptotic properties of conditional least-squares estimators for array time series," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 525-547, October.
    4. Xinyang Wang & Dehui Wang & Kai Yang, 2021. "Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 713-750, July.
    5. Stefan Birr & Stanislav Volgushev & Tobias Kley & Holger Dette & Marc Hallin, 2017. "Quantile spectral analysis for locally stationary time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1619-1643, November.
    6. Regnard, Nazim & Zakoïan, Jean-Michel, 2011. "A conditionally heteroskedastic model with time-varying coefficients for daily gas spot prices," Energy Economics, Elsevier, vol. 33(6), pages 1240-1251.
    7. Kourogenis, Nikolaos & Pittis, Nikitas & Samartzis, Panagiotis, 2024. "Unbounded heteroscedasticity in autoregressive models," The Journal of Economic Asymmetries, Elsevier, vol. 29(C).
    8. Alj, Abdelkamel & Jónasson, Kristján & Mélard, Guy, 2016. "The exact Gaussian likelihood estimation of time-dependent VARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 633-644.
    9. Karanasos, Menelaos & Paraskevopoulos,Alexandros & Canepa, Alessandra, 2020. "Unified Theory for the Large Family of Time Varying Models with Arma Representations: One Solution Fits All," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202008, University of Turin.
    10. repec:dau:papers:123456789/2285 is not listed on IDEAS
    11. Han Li & Kai Yang & Dehui Wang, 2017. "Quasi-likelihood inference for self-exciting threshold integer-valued autoregressive processes," Computational Statistics, Springer, vol. 32(4), pages 1597-1620, December.
    12. Bardet, Jean-Marc & Doukhan, Paul & Wintenberger, Olivier, 2022. "Contrast estimation of time-varying infinite memory processes," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 32-85.
    13. Quentin Giai Gianetto & Hamdi Raïssi, 2015. "Testing Instantaneous Causality in Presence of Nonconstant Unconditional Covariance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 46-53, January.
    14. Yacouba Boubacar Maïnassara & Landy Rabehasaina, 2020. "Estimation of weak ARMA models with regime changes," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 1-52, April.
    15. Nazim Regnard & Jean‐Michel Zakoïan, 2010. "Structure and estimation of a class of nonstationary yet nonexplosive GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(5), pages 348-364, September.
    16. Mélard, Guy, 2022. "An indirect proof for the asymptotic properties of VARMA model estimators," Econometrics and Statistics, Elsevier, vol. 21(C), pages 96-111.
    17. Rajae Azrak & Guy Melard, 2017. "Autoregressive Models with Time-dependent Coefficients. A comparison between Several Approaches," Working Papers ECARES ECARES 2017-48, ULB -- Universite Libre de Bruxelles.
    18. Abdelkamel Alj & Christophe Ley & Guy Melard, 2015. "Asymptotic Properties of QML Estimators for VARMA Models with Time-Dependent Coefficients: Part I," Working Papers ECARES ECARES 2015-21, ULB -- Universite Libre de Bruxelles.
    19. Abdelkamel Alj & Rajae Azrak & Christophe Ley & Guy Mélard, 2017. "Asymptotic Properties of QML Estimators for VARMA Models with Time-dependent Coefficients," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 617-635, September.
    20. Axioglou Christos & Skouras Spyros, 2015. "Asset pricing with flexible beliefs," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(4), pages 415-443, September.
    21. Abdelkamel Alj & Rajae Azrak & Christophe Ley & Guy Melard, 2016. "Technical Appendix to Asymptotic Properties of QML Estimators for VARMA Models with Time-Dependent Coefficients," Working Papers ECARES ECARES 2016-42, ULB -- Universite Libre de Bruxelles.

    More about this item

    Keywords

    Unconditional Lyapunov condition; Conditional Lindeberg condition; Unconditional Lindeberg condition; Conditional Lyapunov condition; Time series analysis;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:eee:ecolet:v:123:y:2014:i:3:p:305-307. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    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.