Sparse Identification and Estimation of High-Dimensional Vector AutoRegressive Moving Averages

Monday, April 23, 2018 - 1:00pm - 1:30pm
Keller 3-180
Ines Wilms (Katholieke Universiteit Leuven)
The Vector AutoRegressive Moving Average (VARMA) model is fundamental
to the study of multivariate time series. However, estimation becomes challenging in
even relatively low-dimensional VARMA models. With growing interest in the simultaneous
modeling of large numbers of marginal time series, many authors have abandoned
the VARMA model in favor of the Vector AutoRegressive (VAR) model, which is seen as a
simpler alternative, both in theory and practice, in this high-dimensional context. However,
even very simple VARMA models can be very complicated to represent using only VAR
modeling. In this talk, we develop a new approach to VARMA identification and propose
a two-phase method for estimation. Our identification and estimation strategies are
linked in their use of sparsity-inducing convex regularizers, which favor VARMA models
that have only a small number of nonzero parameters. The proposed framework has good estimation and forecast accuracy under numerous simulation settings. We illustrate the forecast performance of the sparse VARMA models for demand forecasting. This is joint work with Sumanta Basu, Jacob Bien and David S. Matteson.