## 1.2 Main Purpose

While Bayesian approaches have been widely used in the literature, we note that nonparametric and semiparametric approaches have advantages in the case of high-dimensional VARs with more than several hundreds of time series variables due to their relatively low computational costs (Opgen-Rhein and Strimmer 2007b). Despite of their relatively high computational costs, Bayesian approaches can impose proper assumptions on the multivariate time series data flexibly, such as VAR roots near unity and correlations between noise processes (Lee, Choi, and Kim 2016). In this sense, a semiparametric approach can be a trade-off between nonparametric and parametric approaches (Lee, Choi, and Kim 2016).

In this study, we developed an integrative R package, **VARshrink**, for implementing nonparametric, parametric, and semiparametric approaches for shrinkage estimation of VAR model parameters. By providing a simple interface function, `VARshrink()`

, for running various types of shrinkage estimation methods, the performance of the methods can be easily compared. We note that the package **vars** implemented an ordinary least squares method for VAR models by the function `VAR()`

. The function `VARshrink()`

was built to extend `VAR()`

to shrinkage estimation methods, so that the **VARshrink** package takes advantage of the tools and methods available in the **vars** package. For example, we demonstrate the use of model selection criteria such as AIC and BIC in this paper, where the methods `AIC(), BIC(),`

and `logLik()`

can handle multivariate t-distribution and the effective number of parameters in **VARshrink**.

This paper is a *brief version* of the original manuscript. This paper is organized as follows. In Section 2, we explain the formulation of VAR models in a multivariate regression problem, which simplifies implementation of the package. In Section 3, we describe the common interface function and the four shrinkage estimation methods included in the package. We clearly present closed form expressions for the shrinkage estimators inferred by the shrinkage methods, so that we can indicate the role of the shrinkage intensity parameters in each method. In addition, we explain how the effective number of parameters can be computed for shrinkage estimators. In Section 4, we present numerical experiments using benchmark data and simulated data *briefly* for comparing performances of the shrinkage estimation methods. Discussion and conclusions are provided in Section 5.