Suppose a vector autoregressive moving‐average model is estimated for m observed variables of primary interest for an application and n–m observed secondary variables to aid in the application. An application indicates the variables of primary interest but usually only broadly suggests secondary variables that may or may not be useful. Often, one has many potential secondary variables to choose from but is unsure which ones to include in or exclude from the application. The article proposes a method called weighted‐covariance factor decomposition (WCFD), comparable to Stock and Watson's method here called principle‐components factor decomposition (PCFD), for reducing the secondary variables to fewer factors to obtain a parsimonious estimated model that is more effective in an application. The WCFD method is illustrated in the article by forecasting quarterly observed U.S. real GDP at monthly intervals using monthly observed four coincident and eight leading indicators from the Conference Board (). The results show that root mean‐squared errors of GDP forecasts of PCFD‐factor models are 0.9–11.3% higher than those of WCFD‐factor models especially as estimation‐forecasting periods pass from the pre‐2007 Great Moderation through the 2007–2009 Great Recession to the 2009–2016 Slow Recovery.

中文翻译：

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Varma 模型的加权协方差因子分解应用于按月间隔预测季度美国实际 GDP

假设一个向量自回归移动平均模型被估计为 m 个对应用程序主要感兴趣的观察变量和 n-m 个观察到的次要变量以帮助应用程序。应用程序指出主要感兴趣的变量，但通常只广泛地建议可能有用也可能没用的次要变量。通常，人们有许多潜在的次要变量可供选择，但不确定在应用程序中包含或排除哪些。这篇文章提出了一种称为加权协方差因子分解 (WCFD) 的方法，类似于 Stock 和 Watson 在这里称为主成分因子分解 (PCFD) 的方法，用于将次要变量减少到更少的因子，以获得更有效的简约估计模型在一个应用程序中。WCFD 方法在文章中通过使用会议委员会 (Conference Board) 每月观察到的四个同步指标和八个领先指标按月预测季度观察到的美国实际 GDP 来说明。结果表明，PCFD 因子模型对 GDP 预测的均方根误差比 WCFD 因子模型高 0.9-11.3%，尤其是在估计预测期从 2007 年之前的大缓和到 2007-2009 年大衰退至 2009-2016 年缓慢复苏。