Page 286 - Special Topic Session (STS) - Volume 3

STS544 Jonathan W. et al.

Forecasting quarterly GDP at real-time monthly
intervals using Bayesian Linear Least-Squares

Methods
1
2
Jonathan Weinhagen ; Peter Zadrozny
1 Bureau of Labor Statistics Division of Industrial Prices 2 Massachusetts Avenue, NE, Room
3865 Washington, DC 20212
2 Bureau of Labor Statistics Division of Price Index Number Research 2 Massachusetts Avenue
NE, Room 3105 Washington, DC 20212

Abstract
The paper proposes and illustrates a Bayesian method that requires only
linear least-squares methods for estimating a monthly VAR model of GDP,
employment, and industrial production using quarterly observations on GDP
and monthly observations on employment and industrial production in order
to forecast GDP at monthly intervals, using the latest available monthly real-
time information. The Bayesian method is Theil and Goldberger's (1962) mixed
estimation method that is used to impose equality restrictions on model
coefficients at different degrees of Bayesian tightness (cf., Shiller, 1974;
Litterman, 1986). The restrictions reflect the implication of stationarity that
VAR coefficients of the same variables and the same implied monthly lags
should be equal. The GDP forecasts of the best-forecasting model were about
9% lower in root mean squared error (RMSE) than those of a baseline
univariate AR model. Tight restrictions resulted in slightly worse forecasting
models with higher RMSEs. The methodological contribution of the paper is
that its method of “stacking” a model for mixed-frequency data at the lowest
frequency immediately generalizes to any number and types of frequencies.

1. Introduction
At any moment a forecaster has available only real-time data that have
been released up to that time. Economic data are available at different
frequencies, some at monthly or shorter intervals, others at longer intervals.
For example, GDP is observed quarterly and employment (EP) and industrial
production (IP) data are observed monthly. Different econometric methods
have been used to estimate vector autoregressive moving-average (VARMA)
models with mixed frequency data (MFD). For example, Zadrozny (1990a,b)
first discussed and illustrated estimating a VARMA model of quarterly GNP
and monthly employment using maximum likelihood estimation (MLE) and,
then, using the estimated model and Kalman filtering to forecast the GNP at
monthly intervals. However, MLE, especially applied to MFD, is difficult to

* This work represents the authors’ views and does not necessarily represent any official
positions of BLS.
 Corresponding author.

275 | I S I W S C 2 0 1 9