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Abstract:
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Traditional estimation of graphical model structure assumes that data is drawn i.i.d. from some underlying homogeneous population. Across the multiple domains of economics, neuroscience, and genetics these assumptions have been recognised as unrealistic and given rise to model extensions that permit heterogeneous populations. In this talk, I will discuss a further extension of graphical dependency modelling that allows us to model both temporal and cross-sectional dependency structure. Specifically, I will introduce a new class of sparse locally-stationary wavelet (sLSW) processes and suggest efficient regularised M-estimators for their identification. Constructed in relation to families of non-decimated wavelets, these processes are able to represent a wide variety of time-series with cross-sectional (and time-varying) dependence. One important and useful consequence of the wavelet modelling approach is that dependency structure can be isolated to distinct scale (or aggregation) levels. I will give an overview of some theoretical results and applications to modelling dynamic financial networks.
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