  The standard vector autoregressive (VAR) models suffer from
overparameterization which is a serious issue for high-dimensional time series
data as it restricts the number of variables and lags that can be incorporated
into the model. Several statistical methods, such as the reduced-rank model for
multivariate (multiple) time series (Velu et al., 1986; Reinsel and Velu, 1998;
Reinsel et al., 2022) and the Envelope VAR model (Wang and Ding, 2018), provide
solutions for achieving dimension reduction of the parameter space of the VAR
model. However, these methods can be inefficient in extracting relevant
information from complex data, as they fail to distinguish between relevant and
irrelevant information, or they are inefficient in addressing the rank
deficiency problem. We put together the idea of envelope models into the
reduced-rank VAR model to simultaneously tackle these challenges, and propose a
new parsimonious version of the classical VAR model called the reduced-rank
envelope VAR (REVAR) model. Our proposed REVAR model incorporates the strengths
of both reduced-rank VAR and envelope VAR models and leads to significant gains
in efficiency and accuracy. The asymptotic properties of the proposed
estimators are established under different error assumptions. Simulation
studies and real data analysis are conducted to evaluate and illustrate the
proposed method.
