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Estimating FARIMA models with uncorrelated but non-independent error terms

Author

Listed:
  • Yacouba Boubacar Maïnassara

    (Université Bourgogne Franche-Comté, Laboratoire de mathématiques de Besançon, UMR CNRS 6623)

  • Youssef Esstafa

    (Université Bourgogne Franche-Comté, Laboratoire de mathématiques de Besançon, UMR CNRS 6623)

  • Bruno Saussereau

    (Université Bourgogne Franche-Comté, Laboratoire de mathématiques de Besançon, UMR CNRS 6623)

Abstract

In this paper we derive the asymptotic properties of the least squares estimator (LSE) of fractionally integrated autoregressive moving-average (FARIMA) models under the assumption that the errors are uncorrelated but not necessarily independent nor martingale differences. We relax the independence and even the martingale difference assumptions on the innovation process to extend considerably the range of application of the FARIMA models. We propose a consistent estimator of the asymptotic covariance matrix of the LSE which may be very different from that obtained in the standard framework. A self-normalized approach to confidence interval construction for weak FARIMA model parameters is also presented. All our results are done under a mixing assumption on the noise. Finally, some simulation studies and an application to the daily returns of stock market indices are presented to corroborate our theoretical work.

Suggested Citation

  • Yacouba Boubacar Maïnassara & Youssef Esstafa & Bruno Saussereau, 2021. "Estimating FARIMA models with uncorrelated but non-independent error terms," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 549-608, October.
    • Handle: RePEc:spr:sistpr:v:24:y:2021:i:3:d:10.1007_s11203-021-09243-7
    DOI: 10.1007/s11203-021-09243-7
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