Abstract

Nonstationary processes are ubiquitous in practical applications. Most standard
theory and methods is developed under the assumption of local stationarity;
e.g. that the dependence between process at different time points locally
only depends on the temporal distance between two observations, and that
summaries of dependence can be locally averaged. We discuss inference for
processes that are not locally stationary, but whose covariance properties
are more complex and heterogeneous. In particular we focus on correlation
in frequency, its causes, as well as models and methods for its inference.
Building valid models is complicated by current limited understanding of
frequency domain dependence, a considerable challenge to forming more flexible
models. Our understanding is motivated by real-life applications in oceanography
and neuroscience.

This is joint work with Hernando Ombao (UCI) and Jonathan Lilly (NWRA).