The Three-Pass Regression Filter: A New Approach to Forecasting Using Many Predictors

61 Pages Posted: 22 Jun 2011 Last revised: 16 May 2019

See all articles by Bryan T. Kelly

Bryan T. Kelly

Yale SOM; AQR Capital Management, LLC; National Bureau of Economic Research (NBER)

Seth Pruitt

Arizona State University (ASU) - Finance Department

Date Written: May 1, 2014


We forecast a single time series using many predictor variables with a new estimator called the three-pass regression filter (3PRF). It is calculated in closed form and conveniently represented as a set of ordinary least squares regressions. 3PRF forecasts converge to the infeasible best forecast when both the time dimension and cross section dimension become large. This requires only specifying the number of relevant factors driving the forecast target, regardless of the total number of common (and potentially irrelevant) factors driving the cross section of predictors. We derive inferential theory in the form of limiting distributions for estimated relevant factors, predictive coefficients and forecasts, and provide consistent standard error estimators. We explore two empirical applications that exemplify the many predictor problem: Forecasting macroeconomic aggregates with a large panel of economic indices, and forecasting stock market aggregates with many individual assets' price-dividend ratios. These, combined with a range of Monte Carlo experiments, demonstrate the 3PRF's forecasting power.

Keywords: forecast, many predictors, factor model, Kalman filter, constrained least squares, principal components, partial least squares

Suggested Citation

Kelly, Bryan T. and Pruitt, Seth, The Three-Pass Regression Filter: A New Approach to Forecasting Using Many Predictors (May 1, 2014). Fama-Miller Working Paper; Chicago Booth Research Paper No. 11-19. Available at SSRN: or

Bryan T. Kelly (Contact Author)

Yale SOM ( email )

135 Prospect Street
P.O. Box 208200
New Haven, CT 06520-8200
United States

AQR Capital Management, LLC ( email )

Greenwich, CT
United States

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Seth Pruitt

Arizona State University (ASU) - Finance Department ( email )

W. P. Carey School of Business
PO Box 873906
Tempe, AZ 85287-3906
United States

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