A Direct Estimation of High Dimensional Stationary Vector Autoregressions

Understand

The vector autoregressive (VAR) model is a powerful tool in modeling complex time series and has been exploited in many fields.

• However, fitting high dimensional VAR model poses some unique challenges: On one hand, the dimensionality, caused by modeling a large number of time series and higher order autoregressive processes, is usually much higher than the time series length; On the other hand, the temporal dependence structure in the VAR model gives rise to extra theoretical challenges.
• In high dimensions, one popular approach is to assume the transition matrix is sparse and fit the VAR model using the "least squares" method with a lasso-type penalty.
• In this manuscript, we propose an alternative way in estimating the VAR model.