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The elliptical Ornstein–Uhlenbeck process

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The elliptical Ornstein–Uhlenbeck process. / Sykulski, Adam; Olhede, Sofia Charlotta; Sykulska-Lawrence, Hanna.
In: Statistics and Its Interface, Vol. 16, No. 1, 28.12.2022, p. 133-146.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Sykulski, A, Olhede, SC & Sykulska-Lawrence, H 2022, 'The elliptical Ornstein–Uhlenbeck process', Statistics and Its Interface, vol. 16, no. 1, pp. 133-146. https://doi.org/10.4310/sii.2023.v16.n1.a11

APA

Sykulski, A., Olhede, S. C., & Sykulska-Lawrence, H. (2022). The elliptical Ornstein–Uhlenbeck process. Statistics and Its Interface, 16(1), 133-146. https://doi.org/10.4310/sii.2023.v16.n1.a11

Vancouver

Sykulski A, Olhede SC, Sykulska-Lawrence H. The elliptical Ornstein–Uhlenbeck process. Statistics and Its Interface. 2022 Dec 28;16(1):133-146. doi: 10.4310/sii.2023.v16.n1.a11

Author

Sykulski, Adam ; Olhede, Sofia Charlotta ; Sykulska-Lawrence, Hanna. / The elliptical Ornstein–Uhlenbeck process. In: Statistics and Its Interface. 2022 ; Vol. 16, No. 1. pp. 133-146.

Bibtex

@article{384b92dd730d464b9674b654112b75ac,
title = "The elliptical Ornstein–Uhlenbeck process",
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{\textquoteright}s polar motion.",
keywords = "Oscillations, Complex-valued, Widely Linear, Whittle Likelihood, Polar Motion",
author = "Adam Sykulski and Olhede, {Sofia Charlotta} and Hanna Sykulska-Lawrence",
year = "2022",
month = dec,
day = "28",
doi = "10.4310/sii.2023.v16.n1.a11",
language = "English",
volume = "16",
pages = "133--146",
journal = "Statistics and Its Interface",
issn = "1938-7989",
publisher = "International Press of Boston, Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - The elliptical Ornstein–Uhlenbeck process

AU - Sykulski, Adam

AU - Olhede, Sofia Charlotta

AU - Sykulska-Lawrence, Hanna

PY - 2022/12/28

Y1 - 2022/12/28

N2 - 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.

AB - 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.

KW - Oscillations

KW - Complex-valued

KW - Widely Linear

KW - Whittle Likelihood

KW - Polar Motion

U2 - 10.4310/sii.2023.v16.n1.a11

DO - 10.4310/sii.2023.v16.n1.a11

M3 - Journal article

VL - 16

SP - 133

EP - 146

JO - Statistics and Its Interface

JF - Statistics and Its Interface

SN - 1938-7989

IS - 1

ER -