Change points in heavy-tailed multivariate time series: Methods using precision matrices

摘要

We propose two robust data-driven techniques for detecting network structure change points between heavy-tailed multivariate time series for situations where both the placement and number of change points are unknown. The first technique utilizes the graphical lasso method to estimate the change points, whereas the second technique utilizes the tlasso method. The techniques not only locate the change points but also estimate an undirected graph (or precision matrix) representing the relationship between the time series within each interval created by pairs of adjacent change points. An inference procedure on the edges is used in the graphs to effectively remove false-positive edges, which are caused by the data deviating from normality. The techniques are compared using simulated multivariate t-distributed (heavy-tailed) time series data and the best method is applied to two financial returns data sets of stocks and indices. The results illustrate the method's ability to determine how the dependence structure of the returns changes over time. This information could potentially be used as a tool for portfolio optimization.