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).
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