The Elliptical Ornstein-Uhlenbeck Process
The Elliptical Ornstein-Uhlenbeck Process
We introduce the elliptical Ornstein–Uhlenbeck (OU) process, which is a generalisation of the well-known univariate OU process to bivariate time series. This process maps out elliptical stochastic oscillations over time in the complex plane, which are observed in many applications of coupled bivariate time series. The appeal of the model is that elliptical oscillations are generated using one simple first order stochastic differential equation (SDE), whereas alternative models require more complicated vectorised or higher order SDE representations. The second useful feature is that parameter estimation can be performed semi-parametrically in the frequency domain using the Whittle Likelihood. We determine properties of the model including the conditions for stationarity, and the geometrical structure of the elliptical oscillations. We demonstrate the utility of the model by measuring periodic and elliptical properties of Earth’s polar motion.
Complex-valued, Oscillations, Polar motion, Whittle likelihood, Widely linear
133-146
Sykulski, Adam
e0ee8751-cbb1-47b8-9069-d9b4f50bbda4
Olhede, Sofia
8a72e223-d0ec-4f71-821d-92e2c41e6fd9
Sykulska-Lawrence, Hanna
844512fc-78fb-420c-8d16-fefa2ce35d26
27 July 2022
Sykulski, Adam
e0ee8751-cbb1-47b8-9069-d9b4f50bbda4
Olhede, Sofia
8a72e223-d0ec-4f71-821d-92e2c41e6fd9
Sykulska-Lawrence, Hanna
844512fc-78fb-420c-8d16-fefa2ce35d26
Sykulski, Adam, Olhede, Sofia and Sykulska-Lawrence, Hanna
(2022)
The Elliptical Ornstein-Uhlenbeck Process.
Statistics and Its Interface, 16 (1), .
(doi:10.4310/21-SII714).
Abstract
We introduce the elliptical Ornstein–Uhlenbeck (OU) process, which is a generalisation of the well-known univariate OU process to bivariate time series. This process maps out elliptical stochastic oscillations over time in the complex plane, which are observed in many applications of coupled bivariate time series. The appeal of the model is that elliptical oscillations are generated using one simple first order stochastic differential equation (SDE), whereas alternative models require more complicated vectorised or higher order SDE representations. The second useful feature is that parameter estimation can be performed semi-parametrically in the frequency domain using the Whittle Likelihood. We determine properties of the model including the conditions for stationarity, and the geometrical structure of the elliptical oscillations. We demonstrate the utility of the model by measuring periodic and elliptical properties of Earth’s polar motion.
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SII-2023-0016-0001-a011
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Accepted/In Press date: 29 November 2021
Published date: 27 July 2022
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© 2023. Statistics and its Interface. All Rights Reserved.
Keywords:
Complex-valued, Oscillations, Polar motion, Whittle likelihood, Widely linear
Identifiers
Local EPrints ID: 469705
URI: http://eprints.soton.ac.uk/id/eprint/469705
ISSN: 1938-7989
PURE UUID: d2aaf55a-32f6-4782-bc47-031ec9c59ae8
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Date deposited: 22 Sep 2022 16:43
Last modified: 16 Mar 2024 21:52
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Author:
Adam Sykulski
Author:
Sofia Olhede
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