Vector autoregression and envelope model

Abstract

Vector autoregression is an important technique for modelling multivariate time series and has been widely used in a variety of applications. Owing to its fast growth of parameters with the dimension of the time series vector, dimension reduction is often desirable in multivariate time series analysis. The envelope model is a new approach to achieve dimension reduction and allows efficient estimation in multivariate analysis. In this paper, we provide the first work to explore the application and extension of envelope models to multivariate time series data. We present the envelope and partial envelope formulations for vector autoregression and elaborate model selection, parameter estimation and asymptotic results. Simulations and real data analysis demonstrate the efficiency gains of the envelope vector autoregression models compared with the standard models in terms of estimation. Meanwhile, the envelope models can excel in prediction improvement.