Volume 27, 2023
|Page(s)||156 - 173|
|Published online||20 January 2023|
Fast calibration of weak Farima models
1 Le Mans Université, Institut du Risque et de l’Assurance, Laboratoire Manceau de Mathématiques,
Avenue Olivier Messiaen,
Le Mans Cedex 9,
2 LMAC EA 2222 Université de Technologie de Compiègne CS 60319 - 57 Avenue de Landshut 60203 Compiègne Cedex, France
* Corresponding author: firstname.lastname@example.org
Accepted: 15 December 2022
In this paper, we investigate the asymptotic properties of Le Cam’s one-step estimator for weak Fractionally AutoRegressive Integrated Moving-Average (FARIMA) models. For these models, noises are uncorrelated but neither necessarily independent nor martingale differences errors. We show under some regularity assumptions that the one-step estimator is strongly consistent and asymptotically normal with the same asymptotic variance as the least squares estimator. We show through simulations that the proposed estimator reduces computational time compared with the least squares estimator. An application for providing remotely computed indicators for time series is proposed.
Mathematics Subject Classification: 62M10 / 62M15 / 91B84
Key words: Weak FARIMA models / Le Cam’s one-step estimator / least squares estimator / consistency / asymptotic normality
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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