  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.
