Weighted-Covariance Factor Decomposition of Varma Models Applied to Forecasting Quarterly U.S. Real GDP at Monthly Intervals

Suppose a vector autoregressive moving-average model is estimated for m observed variables of primary interest for an appli-cation 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 sec-ondary 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 parsi-monious 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 (http://www.conference-board.org). The results show that root mean-squared errors of GDP fore-casts 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.