Abstract

Co-authors: Adam Sykulski (UCL), Jonathan Lilly (NWRA), Jeffrey Early (NWRA)

Nonstationarity, like all non-properties, is hard to pin down precisely, and to model sufficiently flexibly for realism, but at the same time model in a sufficiently constrained fashion to allow for good inference. Modelling is inevitably time or frequency domain, where the two branches of thinking are traditionally linked via the local spectrum, or another bilinear representation of the data.

The resolution in the representation is constrained by the choice of representation. There are of course many alternatives to modelling the local Fourier transform, but these have been mainly parametric or have been developed for a specific application.

A problem in general is chosing a representation that suits analysis of more than one series. We shall focus on how our notion of nonstationarity must change when thinking of such observations, focussing on what features are present in bivariate series, that cannot be found in univariate observations.