Estimating FARIMA models with uncorrelated but non-independent error terms

Yacouba Boubacar Maïnassara (), Youssef Esstafa () and Bruno Saussereau ()
Additional contact information
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

Statistical Inference for Stochastic Processes, 2021, vol. 24, issue 3, No 3, 549-608

Abstract: 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.

Keywords: Nonlinear processes; FARIMA models; Least-squares estimator; Consistency; Asymptotic normality; Spectral density estimation; Self-normalization; Cumulants; Primary 62M10; Secondary 91B84 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11203-021-09243-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sistpr:v:24:y:2021:i:3:d:10.1007_s11203-021-09243-7

Ordering information: This journal article can be ordered from
http://www.springer. ... ty/journal/11203/PS2

DOI: 10.1007/s11203-021-09243-7

Access Statistics for this article

Statistical Inference for Stochastic Processes is currently edited by Denis Bosq, Yury A. Kutoyants and Marc Hallin

More articles in Statistical Inference for Stochastic Processes from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().