2011/07/26 by Emily B. Fox, Fox, Emily B., Mike West +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Forecasting Techniques and Applications #Methodology (stat.ME) #stat.ME
paper · pdf · doi:10.48550/arxiv.1107.5239
arxiv created 2011/07/26 · openalex publication_date 2011/07/26 · arxiv updated 2011/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and explore a new class of stationary time series models for variance matrices based on a constructive definition exploiting inverse Wishart distribution theory. The main class of models explored is a novel class of stationary, first-order autoregressive (AR) processes on the cone of positive semi-definite matrices. Aspects of the theory and structure of these new models for multivariate "volatility" processes are described in detail and exemplified. We then develop approaches to model fitting via Bayesian simulation-based computations, creating a custom filtering method that relies on an efficient innovations sampler. An example is then provided in analysis of a multivariate electroencephalogram (EEG) time series in neurological studies. We conclude by discussing potential further developments of higher-order AR models and a number of connections with prior approaches.