Skip to main content
SpringerLink
Log in

Drift estimation for a periodic mean reversion process

  • Published:
Statistical Inference for Stochastic Processes Aims and scope Submit manuscript

Abstract

In this paper we propose a periodic, mean-reverting Ornstein–Uhlenbeck process of the form

$$ dX_t=(L(t)-\alpha\, X_t)\, dt + \sigma\, dB_t, \quad t\geq 0, $$

where L(t) is a periodic, parametric function. We apply maximum likelihood estimation for the drift parameters based on time-continuous observations. The estimator is given explicitly and we prove strong consistency and asymptotic normality as the observed number of periods tends to infinity. The essential idea of the asymptotic study is the interpretation of the stochastic process as a sequence of random variables that take values in some function space.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bishwal JPN (2008) Parameter estimation in stochastic differential equations. Springer-Verlag, Berlin

    Book  MATH  Google Scholar 

  • Gantmacher FR (1986) Matrizentheorie. VEB Deutscher Verlag der Wissenschaften, Berlin

    MATH  Google Scholar 

  • Geman H (2005) Commodities and commodity derivatives. Wiley, Chichester

    Google Scholar 

  • Kuo HH (2006) Introduction to stochastic integrals. Springer-Verlag, New York

    Google Scholar 

  • Kutoyants YA (2004) Statistical inference for ergodic diffusion processes. Springer-Verlag, London

    MATH  Google Scholar 

  • Lax PD (2002) Functional analysis. Wiley, New York

    MATH  Google Scholar 

  • Lipster RS, Shiryayev AN (1977) Statistics of random processes I. Springer-Verlag, Berlin

    Google Scholar 

  • Øksendal B (2003) Stochastic Differential Equations. Springer-Verlag, Berlin

    Google Scholar 

  • Ornstein LS, Uhlenbeck GE (1930) On the theory of Brownian motion. Phys Rev 36: 823–841

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität Bochum, NA 3/33, 44780, Bochum, Germany

    Herold Dehling, Brice Franke & Thomas Kott

Authors
  1. Herold Dehling
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Brice Franke
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Thomas Kott
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Herold Dehling.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dehling, H., Franke, B. & Kott, T. Drift estimation for a periodic mean reversion process. Stat Inference Stoch Process 13, 175–192 (2010). https://doi.org/10.1007/s11203-010-9045-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11203-010-9045-8

Keywords

Search

Navigation