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On conditions in central limit theorems for martingale difference arrays

Author

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  • 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
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    References listed on IDEAS

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    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)

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    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).
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    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.

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    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

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