Chi-Squared Tests for Evaluation and Comparison of Asset Pricing Models

Nikolay Gospodinov, Raymond Kan, and Cesare Robotti
Working Paper 2011-8
March 2011

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This paper presents a general statistical framework for estimation, testing, and comparison of asset pricing models using the unconstrained distance measure of Hansen and Jagannathan (1997). The limiting results cover both linear and nonlinear models that could be correctly specified or misspecified. We propose new pivotal specification and model comparison tests that are asymptotically chi-squared distributed. In addition, we develop modified versions of the existing model selection tests with improved finite-sample properties. Finally, we fill an important gap in the literature by providing formal tests of multiple model comparison.

JEL classification: C12, C13, G12

Key words: asset pricing models, Hansen-Jagannathan distance, model selection, model misspecification

Nikolay Gospodinov gratefully acknowledges financial support from Fonds de recherche sur la société et la culture (FQRSC), Institut de Finance Mathématique de Montréal (IFM2), and the Social Sciences and Humanities Research Council of Canada. Raymond Kan gratefully acknowledges financial support from the National Bank Financial of Canada, the Social Sciences and Humanities Research Council of Canada, and the Center for Financial Innovation and Stability at the Federal Reserve Bank of Atlanta. The authors thank Esther Eiling, Wayne Ferson, Jonathan Fletcher, Eric Jondeau, B. Ravikumar, Sergei Sarkissian, Jonathan Wright, Chu Zhang, Guofu Zhou, seminar participants at EDHEC Business School, Emory University, HEC Lausanne, University of Montreal, and participants at the 2010 IFM2 Symposium on Mathematical Finance, the 2010 Meetings of the Society for Nonlinear Dynamics and Econometrics, and the 2010 NBER-NSF Time Series Conference for helpful discussions and comments. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions regarding content to Nikolay Gospodinov, Concordia University and CIREQ, Department of Economics, 1455 de Maisonneuve Boulevard West, Montreal, Quebec, Canada H3G 1M8, 514-848-2424 (ex. 3935), 514-848-4536 (fax),; Raymond Kan, University of Toronto, Joseph L. Rotman School of Management, 105 St. George Street, Toronto, Ontario, Canada M5S 3E6, 416-978-4291, 416-978-5433,; or Cesare Robotti (corresponding author), Federal Reserve Bank of Atlanta and EDHEC Risk Institute, Research Department, 1000 Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-8543, 404-498-8810 (fax),

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