The Annals of Statistics
- Ann. Statist.
- Volume 31, Number 6 (2003), 1772-1821.
Estimating deformations of stationary processes
This paper studies classes of nonstationary processes, such as warped processes and frequency-modulated processes, that result from the deformation of stationary processes. Estimating deformations can often provide important information about an underlying physical phenomenon. A computational harmonic analysis viewpoint shows that the deformed autocovariance satisfies a transport equation at small scales, with a velocity proportional to a deformation gradient. We derive an estimator of the deformation from a single realization of the deformed process, with a proof of consistency under appropriate assumptions.
Ann. Statist., Volume 31, Number 6 (2003), 1772-1821.
First available in Project Euclid: 16 January 2004
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 60G12: General second-order processes
Secondary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]
Clerc, Maureen; Mallat, Stéphane. Estimating deformations of stationary processes. Ann. Statist. 31 (2003), no. 6, 1772--1821. doi:10.1214/aos/1074290327. https://projecteuclid.org/euclid.aos/1074290327