Nonparametric estimation for i.i.d. Gaussian continuous time moving average models

Fabienne Comte () and Valentine Genon-Catalot ()
Additional contact information
Fabienne Comte: Université de Paris, CNRS, MAP5 UMR 8145
Valentine Genon-Catalot: Université de Paris, CNRS, MAP5 UMR 8145

Statistical Inference for Stochastic Processes, 2021, vol. 24, issue 1, No 5, 149-177

Abstract: Abstract We consider a Gaussian continuous time moving average model $$X(t)=\int _0^t a(t-s)dW(s)$$ X ( t ) = ∫ 0 t a ( t - s ) d W ( s ) where W is a standard Brownian motion and a(.) a deterministic function locally square integrable on $${{\mathbb {R}}}^+$$ R + . Given N i.i.d. continuous time observations of $$(X_i(t))_{t\in [0,T]}$$ ( X i ( t ) ) t ∈ [ 0 , T ] on [0, T], for $$i=1, \dots , N$$ i = 1 , ⋯ , N distributed like $$(X(t))_{t\in [0,T]}$$ ( X ( t ) ) t ∈ [ 0 , T ] , we propose nonparametric projection estimators of $$a^2$$ a 2 under different sets of assumptions, which authorize or not fractional models. We study the asymptotics in T, N (depending on the setup) ensuring their consistency, provide their nonparametric rates of convergence on functional regularity spaces. Then, we propose a data-driven method corresponding to each setup, for selecting the dimension of the projection space. The findings are illustrated through a simulation study.

Keywords: Continuous time moving average; Gaussian processes; Model selection; Nonparametric estimation; Projection estimators; 62G05; 62M09 (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/s11203-020-09228-y 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:1:d:10.1007_s11203-020-09228-y

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

DOI: 10.1007/s11203-020-09228-y

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 ().