Ridge regression is a popular regularization method that has wide applicability, as many regression problems can be cast in this form. However, ridge is only seldom applied in the estimation of vector autoregressive models, even though it naturally arises in Bayesian time series modeling. In this work, ridge regression is studied in the context of process estimation and inference of VARs. The effects of shrinkage are analyzed and asymptotic theory is derived enabling inference. Frequentist and Bayesian ridge approaches are compared. Finally, the estimation of impulse response functions is evaluated with Monte Carlo simulations and ridge regression is compared with a number of similar and competing methods.

翻译：岭回归是一种广泛适用的流行正则化方法，许多回归问题均可转化为该形式。然而，尽管贝叶斯时间序列建模中自然涉及岭回归，该方法在向量自回归模型估计中的应用仍较为罕见。本文研究了岭回归在VAR过程估计与推断中的表现，分析了收缩效应并推导了支持推断的渐近理论，同时比较了频率学派与贝叶斯岭回归方法。最后，通过蒙特卡洛模拟评估了脉冲响应函数的估计效果，并将岭回归与若干相似及竞争方法进行了对比。