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

• Activity Number: 161 - Advances in Forecasting of Macroeconomic Variables: New Methods and Applications
• Type: Topic Contributed
• Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Peter Zadrozny* and Baoline Chen
• Companies: Bureau of Labor Statistics and Bureau of Economic Analysis
• Keywords: principal components; factor decomposition; mutivariate time series

Abstract

A vector autoregressive moving-average (VARMA) 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 variables of primary interest but usually only broadly suggests possibly useful secondary variables. One can choose many potential secondary variables but is unsure which to include in or exclude from an application. The paper proposes a method called weighted-covariance factor decomposition (WCFD), comparable to principle-components factor decomposition (PCFD), for reducing secondary variables to fewer factors to obtain a more parsimonious and effective estimated model in an application. The WCFD method is illustrated by forecasting quarterly-observed U.S. real GDP at monthly intervals using monthly-observed 4 coincident and 8 leading indicators from the Conference Board (2018). 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.