A local vector autoregressive framework and its applications to multivariate time series monitoring and forecasting

Abstract

Our proposed local vector autoregressive (LVAR) model has time-varying parameters that allow it to be safely used in both stationary and non-stationary situations. The estimation is conducted over an interval of local homogeneity where the parameters are approximately constant. The local interval is identified in a sequential testing procedure. Numerical analysis and real data applications are conducted to illustrate the monitoring function and forecast performance of the proposed model.

Adaptive, locally linear models of complex dynamics

“…Principled approaches for the segmentation of time series include those of change-point detection [13][14][15][16][17][18][19][20], which aim to identify structural changes in the time series but often focus on the location of change-points or forecasting, instead of the underlying dynamics [15][16][17][18][19][20]. Other techniques such as hidden Markov models [21][22][23], assume that the global dynamics are composed of a set of underlying dynamical states which the system revisits, without providing a parameterization of the underlying dynamical patterns [23].…”