Weighted-Covariance Reduction of Vector Autoregressive Moving Average Models

• Activity Number: 119
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 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: model reduction ; dynamic factor models ; principal components

Abstract

We develop and apply a method for reducing an estimated VARMA model of observed variables being considered to a smaller VARMA model of a subset of observed variables of primary interest. Although WCR is closely related to principal components analysis (PCA), it has 3 different features: (1) whereas PCA applies only to stationary data, WCR applies to any mixture of stationary and nonstationary data and models; (2) whereas PCA implicitly takes a long run perspective, in WCR the user sets a time perspective of any finite duration; (3) like PCA, WCR could be used to reduce data to factors, but, unlike PCA, also reduces models of initial variables to smaller models of a subset of observed variables of primary interest. We illustrate WCR with quarterly U.S. data on 14 macroeconomic idicators and real GDP. We estimate models in log and differenced-log forms, apply WCR to the estimated models, determine the number of significant factors for each model; reduce each model to a univariate GDP model; and compare the estimated and reduced models in terms of RMSEs of out-of-sample GDP forecasts.