# VARshrink v0.3.1

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## Shrinkage Estimation Methods for Vector Autoregressive Models

Vector autoregressive (VAR) model is a fundamental and effective approach for multivariate time series analysis. Shrinkage estimation methods can be applied to high-dimensional VAR models with dimensionality greater than the number of observations, contrary to the standard ordinary least squares method. This package is an integrative package delivering nonparametric, parametric, and semiparametric methods in a unified and consistent manner, such as the multivariate ridge regression in Golub, Heath, and Wahba (1979) <doi:10.2307/1268518>, a James-Stein type nonparametric shrinkage method in Opgen-Rhein and Strimmer (2007) <doi:10.1186/1471-2105-8-S2-S3>, and Bayesian estimation methods using noninformative and informative priors in Lee, Choi, and S.-H. Kim (2016) <doi:10.1016/j.csda.2016.03.007> and Ni and Sun (2005) <doi:10.1198/073500104000000622>.

# VARshrink: Shrinkage Estimation Methods for Vector Autoregressive (VAR) Models.

VAR model is a fundamental and effective approach for multivariate time series analysis. Shrinkage estimation methods can be applied to high-dimensional VAR models with dimensionality greater than the number of observations, contrary to the standard ordinary least squares method.

The package VARshrink aims to be an integrative R package delivering nonparametric, parametric, and semiparametric methods in a unified and consistent manner.

The package VARshrink provides a simple interface function VARshrink(), which is an extension of the function VAR() in the vars package.

Example:

data(Canada, package = "vars")
estim <- VARshrink(y, p = 2, type = "const", method = "ns")
plot(predict(estim), names = "U")


### References

N. Lee, H. Choi, and S.-H. Kim (2016). Bayes shrinkage estimation for high-dimensional VAR models with scale mixture of normal distributions for noise. Computational Statistics & Data Analysis 101, 250-276. doi: 10.1016/j.csda.2016.03.007

S. Ni and D. Sun (2005). Bayesian estimates for vector autoregressive models. Journal of Business & Economic Statistics 23(1), 105-117. doi: 10.1198/073500104000000622

R. Opgen-Rhein and K. Strimmer (2007). Learning causal networks from systems biology time course data: an effective model selection procedure for the vector autoregressive process. BMC Bioinformatics 8(2), S3. doi: 10.1186/1471-2105-8-S2-S3.

## Functions in VARshrink

 Name Description lm_multiv_ridge Multivariate Ridge Regression lm_full_Bayes_SR Full Bayesian Shrinkage Estimation Method for Multivariate Regression lm_ShVAR_KCV K-fold Cross Validation for Selection of Shrinkage Parameters of Semiparametric Bayesian Shrinkage Estimator for Multivariate Regression irf.varshrinkest Impulse response function restrict_sh Restricted VAR arch.test_sh ARCH-LM test print.varshsum Print method for class "varshsum" fevd.varshrinkest Forecast Error Variance Decomposition normality.test_sh Normality, multivariate skewness and kurtosis test logLik.varshrinkest Log-likelihood method for class "varshrinkest" roots_sh Eigenvalues of the companion coefficient matrix of a VAR(p)-process serial.test_sh Test for serially correlated errors for VAR shrinkage estimate predict.varshrinkest Predict method for objects of class varshrinkest lm_semi_Bayes_PCV Semiparametric Bayesian Shrinkage Estimation Method for Multivariate Regression stability_sh Stability function summary.shrinklm Summary method for class "shrinklm" summary.varshrinkest Summary method for an object of class 'varshrinkest', VAR parameters estimated by VARshrink() simVARmodel Generate multivariate time series data using the given VAR model shrinkVARcoef Semiparametric Bayesian Shrinkage Estimator for Multivariate Regression print.varshrinkest Print method for class "varshrinkest" Acoef_sh Coefficient matrices of endogenous variables causality_sh Causality Analysis for class "varshrinkest" calcSSE_Acoef Sum of squared errors (SSE) between coefficients of two VARs BQ_sh BQ function for class "varshrinkest" convPsi2varresult Convert format for VAR coefficients from Psi to varresult Phi.varshrinkest Coefficient matrices of the MA represention Bcoef_sh Coefficient matrix createVARCoefs_ltriangular Create coefficients of a VAR model VARshrink Shrinkage estimation of VAR parameters No Results!