An Efficient ADMM Algorithm for Structural Break Detection in Multivariate Time Series
This work provides a faster method for researchers and practitioners analyzing non-stationary time series, but it is incremental as it builds on existing convex estimation frameworks.
The authors tackled the problem of detecting structural breaks in multivariate time series by developing an efficient ADMM algorithm that segments the series into stationary regions, achieving a solution time linear in the series length.
We present an efficient alternating direction method of multipliers (ADMM) algorithm for segmenting a multivariate non-stationary time series with structural breaks into stationary regions. We draw from recent work where the series is assumed to follow a vector autoregressive model within segments and a convex estimation procedure may be formulated using group fused lasso penalties. Our ADMM approach first splits the convex problem into a global quadratic program and a simple group lasso proximal update. We show that the global problem may be parallelized over rows of the time dependent transition matrices and furthermore that each subproblem may be rewritten in a form identical to the log-likelihood of a Gaussian state space model. Consequently, we develop a Kalman smoothing algorithm to solve the global update in time linear in the length of the series.