University College London - Statistical Science
This talk will focus on nonstationary time series, from both a methodological and applied perspective. On the methodology side, I will discuss new stochastic models for capturing structure in bivariate data, by representing the series as complex-valued. This representation allows for novel ways of capturing features that are multiscale, anisotropic and/or nonstationary. I will also present new methodology and theory for maximum likelihood inference in the frequency-domain, specifically by providing a method for removing estimation error from the Whittle likelihood.
The application focus will be in oceanography, in particular the analysis of data from the Global Drifter Program. The analysis of this dataset is important for understanding ocean variability and its impact on the climate. We construct physically motivated stochastic processes to describe the data, whose parameters are estimated using locally stationary time series methods. This allows for high-resolution temporal and spatial summary statistics. I will discuss generalizations that can capture anisotropic flow that is typically observed in oceanographic data.