OPTIMAL MULTISTEP VAR FORECAST AVERAGING
提出了基于多元Mallows模型平均和留h折交叉验证平均的多步预测平均方法，适用于向量自回归模型，并证明了其渐近无偏性和最优性。
This article proposes frequentist multiple-equation least-squares averaging approaches for multistep forecasting with vector autoregressive (VAR) models. The proposed VAR forecast averaging methods are based on the multivariate Mallows model averaging (MMMA) and multivariate leave- h -out cross-validation averaging (MCVA h ) criteria (with h denoting the forecast horizon), which are valid for iterative and direct multistep forecast averaging, respectively. Under the framework of stationary VAR processes of infinite order, we provide theoretical justifications by establishing asymptotic unbiasedness and asymptotic optimality of the proposed forecast averaging approaches. Specifically, MMMA exhibits asymptotic optimality for one-step-ahead forecast averaging, whereas for direct multistep forecast averaging, the asymptotically optimal combination weights are determined separately for each forecast horizon based on the MCVA h procedure. To present our methodology, we investigate the finite-sample behavior of the proposed averaging procedures under model misspecification via simulation experiments.