Sparsity-Promoting Bayesian Dynamic Linear Models

Sparsity-promoting priors have become increasingly popular over recent years due to an increased number of regression and classification applications involving a large number of predictors. In time series applications where observations are collected over time, it is often unrealistic to assume that the underlying sparsity pattern is fixed. We propose here an original class of flexible Bayesian linear models for dynamic sparsity modelling. The proposed class of models expands upon the existing Bayesian literature on sparse regression using generalized multivariate hyperbolic distributions. The properties of the models are explored through both analytic results and simulation studies. We demonstrate the model on a financial application where it is shown that it accurately represents the patterns seen in the analysis of stock and derivative data, and is able to detect major events by filtering an artificial portfolio of assets

Bayesian forecasting and scalable multivariate volatility analysis using simultaneous graphical dynamic models

The recently introduced class of simultaneous graphical dynamic linear models (SGDLMs) defines an ability to scale on-line Bayesian analysis and forecasting to higher-dimensional time series. This paper advances the methodology of SGDLMs, developing and embedding a novel, adaptive method of simultaneous predictor selection in forward filtering for on-line learning and forecasting. The advances include developments in Bayesian computation for scalability, and a case study in exploring the resulting potential for improved short-term forecasting of large-scale volatility matrices. A case study concerns financial forecasting and portfolio optimization with a 400-dimensional series of daily stock prices. Analysis shows that the SGDLM forecasts volatilities and co-volatilities well, making it ideally suited to contributing to quantitative investment strategies to improve portfolio returns. We also identify performance metrics linked to the sequential Bayesian filtering analysis that turn out to define a leading indicator of increased financial market stresses, comparable to but leading the standard St. Louis Fed Financial Stress Index (STLFSI) measure. Parallel computation using GPU implementations substantially advance the ability to fit and use these models.Comment: 28 pages, 9 figures, 7 table

Regularized estimation of linear functionals of precision matrices for high-dimensional time series

This paper studies a Dantzig-selector type regularized estimator for linear functionals of high-dimensional linear processes. Explicit rates of convergence of the proposed estimator are obtained and they cover the broad regime from i.i.d. samples to long-range dependent time series and from sub-Gaussian innovations to those with mild polynomial moments. It is shown that the convergence rates depend on the degree of temporal dependence and the moment conditions of the underlying linear processes. The Dantzig-selector estimator is applied to the sparse Markowitz portfolio allocation and the optimal linear prediction for time series, in which the ratio consistency when compared with an oracle estimator is established. The effect of dependence and innovation moment conditions is further illustrated in the simulation study. Finally, the regularized estimator is applied to classify the cognitive states on a real fMRI dataset and to portfolio optimization on a financial dataset.Comment: 44 pages, 4 figure