Sparse and Time-varying Covariance Modeling
Resumo: In many areas there has been a growing interest in developing methods that can estimate dependency of multivariate time series data. Nevertheless, the estimation of a high-dimensional covariance matrix which potentially varies over time is still an open problem. In this work, we discuss several bayesian regularization methods based on shrinkage and variable selection priors and estimate sparse covariance matrices using the modified Cholesky decomposition. Our first application considers time-varying observational variances (stochastic volatility) and uses the Normal-Gamma prior for shrinking the regression coefficients that compose the Cholesky factor. The second application considers homoscedastic errors and time varying regression coefficients which are shrunken by applying an extension of the Normal Mixture of Inverse Gammas (NMIG) hierarchical prior for dynamic models, which accommodates time varying sparsity.
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