Weighted-covariance Factor Decomposition of Varma Models Applied to Forecasting Quarterly U.s. Gdp at Monthly Intervals

We develop and apply a method, called weighted-covariance factor decomposition (WCD), for reducing large estimated vector autoregressive moving-average (VARMA) data models of many "important" and "unimportant" variables to smaller VARMAfactor models of "important" variables and significant factors. WCD has four particularly notable features, compared to frequently used principal components decomposition, for developing parsimonious dynamic models: (1) WCD reduces larger VARMA-data models of "important" and "unimportant" variables to smaller VARMA-factor models of "important" variables, while still accounting for all significant covariances between "important" and "unimportant" variables; (2) WCD allows any mixture of stationary and nonstationary variables; (3) WCD produces factors, which can be used to estimate VARMA-factor models, but more directly reduces VARMA-data models to VARMA-factor models; and, (4) WCD leads to a modelbased asymptotic statistical test for the number of significant factors. We illustrate WCD with U.S. monthly indicators (4 coincident, 10 leading) and quarterly real GDP. We estimate 4 monthly VARMA-data models of 5 and 11 variables, in log and percentage-growth form; we apply WCD to the 4 data models; we test each data model for the number of significant factors; we reduce each data model to a significant-factor model; and, we use the data and factor models to compute out-of-sample monthly GDP forecasts and evaluate their accuracy. The application's main conclusion is that WCD can reduce moderately large VARMA-data models of "important" GDP and up to 10 "unimportant" indicators to small univariate-ARMA-factor models of GDP which forecast GDP almost as accurately as the larger data models.