Analysis of nonstationary modulated time series with applications to oceanographic flow measurements

TL;DR

This paper introduces a new nonstationary time series model framework suitable for rapidly changing data and missing observations, with applications to oceanographic flow measurements and climate analysis.

Contribution

It develops a novel modulated time series model and an efficient Whittle-likelihood based inference method for nonstationary and isotropic bivariate data.

Findings

The proposed model effectively captures nonstationary oceanographic data.

The inference method is computationally efficient and consistent.

Application demonstrates utility in climate and ocean circulation studies.

Abstract

We propose a new class of univariate nonstationary time series models, using the framework of modulated time series, which is appropriate for the analysis of rapidly-evolving time series as well as time series observations with missing data. We extend our techniques to a class of bivariate time series that are isotropic. Exact inference is often not computationally viable for time series analysis, and so we propose an estimation method based on the Whittle-likelihood, a commonly adopted pseudo-likelihood. Our inference procedure is shown to be consistent under standard assumptions, as well as having considerably lower computational cost than exact likelihood in general. We show the utility of this framework for the analysis of drifting instruments, an analysis that is key to characterising global ocean circulation and therefore also for decadal to century-scale climate understanding.