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Asymptotic properties of conditional least-squares estimators for array time series

Author

Listed:
  • Rajae Azrak

    (Mohammed V University of Rabat)

  • Guy Mélard

    (Université libre de Bruxelles)

Abstract

The paper provides a kind of Klimko–Nelson’s theorems alternative in the case of conditional least-squares and M-estimators for array time series when the assumptions of almost sure convergence cannot be established. We do not assume stationarity nor even local stationarity. Besides, we provide sufficient conditions for two of the assumptions and a procedure for the evaluation of the information matrix in array time series. In addition to time-dependent models, illustrations to a threshold model and a count data model are given.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sistpr:v:24:y:2021:i:3:d:10.1007_s11203-021-09242-8
    DOI: 10.1007/s11203-021-09242-8
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    References listed on IDEAS

    as
    1. Doukhan, Paul & Fokianos, Konstantinos & Tjøstheim, Dag, 2012. "On weak dependence conditions for Poisson autoregressions," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 942-948.
    2. 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.
    3. Richard A. Davis, 2003. "Observation-driven models for Poisson counts," Biometrika, Biometrika Trust, vol. 90(4), pages 777-790, December.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
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    Cited by:

    1. 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.

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