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Activity Number: 345
Type: Topic Contributed
Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #307961
Title: Locally Adaptive Bayesian Covariance Regression
Author(s): Daniele Durante*+ and Bruno Scarpa and David B. Dunson
Companies: Department of Statistical Sciences, University of Padua and Department of Statistical Sciences, University of Padua and Duke University
Keywords: Bayesian nonparametrics ; locally varying smoothness ; multivariate time series ; nested Gaussian process ; stochastic volatility
Abstract:

Multivariate time series data arise in many applied domains, and it is often crucial to obtain a good characterization of how the covariance among the different variables changes over time. This is the case in financial applications in which covariance can change dramatically during financial crisis, revealing different associations among assets than occur in a healthier economic climate. Our focus is on developing models that allow the covariance to vary flexibly over continuous time, and additionally accommodate locally adaptive smoothing of the covariance. Locally adaptive smoothing to accommodate varying smoothness in a trajectory has been well studied, but such approaches have not yet been developed for time-varying covariance matrices to our knowledge. To address this gap, we generalize recently develop methods for Bayesian covariance regression to incorporate random dictionary elements with locally varying smoothness. Using a differential equation representation, we develop a fast computational approach via MCMC, with online algorithms also considered. The performance of the models is assessed through simulation studies and the methods are applied to financial time series.


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