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Estimation of weak ARMA models with regime changes

  • Yacouba Boubacar MaïnassaraEmail author
  • Landy Rabehasaina
Article

Abstract

In this paper we derive the asymptotic properties of the least squares estimator (LSE) of autoregressive moving-average (ARMA) models with regime changes under the assumption that the errors are uncorrelated but not necessarily independent. Relaxing the independence assumption considerably extends the range of application of the class of ARMA models with regime changes. Conditions are given for the consistency and asymptotic normality of the LSE. A particular attention is given to the estimation of the asymptotic covariance matrix, which may be very different from that obtained in the standard framework. The theoretical results are illustrated by means of Monte Carlo experiments.

Keywords

Least square estimation Random coefficients Weak ARMA models 

Mathematics Subject Classification

Primary 62M10 62F03 62F05 Secondary 91B84 62P05 

Notes

Acknowledgements

We sincerely thank the anonymous reviewers and Editor in Chief for helpful remarks. The authors wish to acknowledge the support from the “Séries temporelles et valeurs extrêmes : théorie et applications en modélisation et estimation des risques” Projet Région grant No OPE-2017-0068.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Laboratoire de mathématiques de Besançon, UMR CNRS 6623Université Bourgogne Franche-ComtéBesançonFrance

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