  This article introduces the sparse group fused lasso (SGFL) as a statistical
framework for segmenting sparse regression models with multivariate time
series. To compute solutions of the SGFL, a nonsmooth and nonseparable convex
program, we develop a hybrid optimization method that is fast, requires no
tuning parameter selection, and is guaranteed to converge to a global
minimizer. In numerical experiments, the hybrid method compares favorably to
state-of-the-art techniques with respect to computation time and numerical
accuracy; benefits are particularly substantial in high dimension. The method's
statistical performance is satisfactory in recovering nonzero regression
coefficients and excellent in change point detection. An application to air
quality data is presented. The hybrid method is implemented in the R package
sparseGFL available on the author's Github page.
