You likely want to do this in real time which means you want to do a nowcasting. This is tricky because many economic series are revised, which means you also need real time data (what were the figures when released rather than what is known with hindsight).
The Atlanta Federal Reserve Bank uses this approach in their GDP Now product. You should check out their methodology and inputs to get started on your attempt.
The growth rate of real gross domestic product (GDP) measured by the
U.S. Bureau of Economic Analysis (BEA) is a key metric of the pace of
economic activity. It is one of the four variables included in the
economic projections of Federal Reserve Board members and Bank
presidents for every other Federal Open Market Committee (FOMC)
meeting. As with many economic statistics, GDP estimates are released
with a lag whose timing can be important for policymakers. For
example, of the four scheduled 2014 release dates of an “advance” (or
first) estimate of GDP growth, two are on the second day of a
scheduled FOMC meeting with the other two on the day after the
meeting. In preparation for FOMC meetings, policymakers have the Fed
Board staff projection of this “advance” estimate at their disposal.
These projections—available through 2008 at the Philadelphia Fed’s
Real Time Data Center—have generally been more accurate than forecasts
from simple statistical models. As stated by economists Jon Faust and
Jonathan H. Wright in a 2009 paper, “by mirroring key elements of the
data construction machinery of the Bureau of Economic Analysis, the
Fed staff forms a relatively precise estimate of what BEA will
announce for the previous quarter’s GDP even before it is announced.”
The Atlanta Fed GDPNow model also mimics the methods used by the BEA
to estimate real GDP growth. The GDPNow forecast is constructed by
aggregating statistical model forecasts of 13 subcomponents that
comprise GDP. Other private forecasters use similar approaches to
“nowcast” GDP growth. However, these forecasts are not updated more
than once a month or quarter, are not publicly available, or do not
have forecasts of the subcomponents of GDP that add “color” to the
top-line number. The Atlanta Fed GDPNow model fills these three voids.
The BEA’s advance estimates of the subcomponents of GDP use publicly
released data from the U.S. Census Bureau, U.S. Bureau of Labor
Statistics, and other sources. Much of this data is displayed in the
BEA’s Key Source Data and Assumptions table that accompanies the
“advance” GDP estimate. GDPNow relates these source data to their
corresponding GDP subcomponents using a “bridge equation” approach
similar to the one described in a Minneapolis Fed study by Preston J.
Miller and Daniel M. Chin. Whenever the monthly source data is not
available, the missing values are forecasted using econometric
techniques similar to those described in papers by James H. Stock and
Mark W. Watson and Domenico Giannone, Lucrezia Reichlin, and David
Small. A detailed description of the data sources and methods used in
the GDPNow model is provided in an accompanying Atlanta Fed working
paper.
As more monthly source data becomes available, the GDPNow forecast for
a particular quarter evolves and generally becomes more accurate. That
said, the forecasting error can still be substantial just prior to the
“advance” GDP estimate release. It is important to emphasize that the
Atlanta Fed GDPNow forecast is a model projection not subject to
judgmental adjustments. It is not an official forecast of the Federal
Reserve Bank of Atlanta, its president, the Federal Reserve System, or
the FOMC.