Electronic Journal of Statistics

Inference for a mean-reverting stochastic process with multiple change points

Fuqi Chen, Rogemar Mamon, and Matt Davison

Full-text: Open access

Abstract

The use of an Ornstein-Uhlenbeck (OU) process is ubiquitous in business, economics and finance to capture various price processes and evolution of economic indicators exhibiting mean-reverting properties. The time at which structural transition representing drastic changes in the economic dynamics occur are of particular interest to policy makers, investors and financial product providers. This paper addresses the change-point problem under a generalised OU model and investigates the associated statistical inference. We propose two estimation methods to locate multiple change points and show the asymptotic properties of the estimators. An informational approach is employed in detecting the change points, and the consistency of our methods is also theoretically demonstrated. Estimation is considered under the setting where both the number and location of change points are unknown. Three computing algorithms are further developed for implementation. The practical applicability of our methods is illustrated using simulated and observed financial market data.

Article information

Source
Electron. J. Statist., Volume 11, Number 1 (2017), 2199-2257.

Dates
Received: April 2016
First available in Project Euclid: 23 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1495504915

Digital Object Identifier
doi:10.1214/17-EJS1282

Mathematical Reviews number (MathSciNet)
MR3654824

Zentralblatt MATH identifier
1364.60045

Subjects
Primary: 60G20: Generalized stochastic processes 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 62M99: None of the above, but in this section

Keywords
Ornstein-Uhlenbeck process sequential analysis least sum of squared errors maximum likelihood consistent estimator segment neighbourhood search method PELT algorithm

Rights
Creative Commons Attribution 4.0 International License.

Citation

Chen, Fuqi; Mamon, Rogemar; Davison, Matt. Inference for a mean-reverting stochastic process with multiple change points. Electron. J. Statist. 11 (2017), no. 1, 2199--2257. doi:10.1214/17-EJS1282. https://projecteuclid.org/euclid.ejs/1495504915


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