General Aggregation of Misspecified Asset Pricing Models

This paper proposes an entropy-based approach for aggregating information from misspecified asset pricing models. The statistical paradigm is shifted away from parameter estimation of an optimally selected model to stochastic optimization based on a risk function of aggregation across models. The proposed method relaxes the perfect substitutability of the candidate models, which is implicitly embedded in the linear pooling procedures, and ensures that the aggregation weights are selected with a proper (Hellinger) distance measure that satisfies the triangle inequality. The empirical results illustrate the robustness and the pricing ability of the aggregation approach to stochastic discount factor models.

[1]  L. Hansen,et al.  Uncertainty Outside and Inside Economic Models , 2014 .

[2]  S. Hall,et al.  Combining density forecasts , 2007 .

[3]  E. Fama,et al.  Common risk factors in the returns on stocks and bonds , 1993 .

[4]  Gianni Amisano,et al.  Prediction with Misspecied Models , 2011 .

[5]  J. Geweke,et al.  Optimal Prediction Pools , 2008 .

[6]  Nikolay Gospodinov,et al.  Chi-Squared Tests for Evaluation and Comparison of Asset Pricing Models , 2012 .

[7]  Yuichi Kitamura,et al.  Connections between Entropic and Linear Projections in Asset Pricing Estimation , 2002 .

[8]  Lucien Birg'e.  Model selection for density estimation with L2-loss , 2008, 0808.1416.

[9]  Timothy R. C. Read,et al.  Multinomial goodness-of-fit tests , 1984 .

[10]  Fousseni Chabi-Yo,et al.  New Entropy Restrictions and the Quest for Better Specified Asset Pricing Models , 2014 .

[11]  Xiaohong Chen,et al.  Land of addicts? an empirical investigation of habit-based asset pricing models , 2009 .

[12]  Ravi Jagannathan,et al.  Implications of Security Market Data for Models of Dynamic Economies , 1990, Journal of Political Economy.

[13]  Stanley E. Zin,et al.  Sources of Entropy in Representative Agent Models , 2011 .

[14]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[15]  N. Reid,et al.  AN OVERVIEW OF COMPOSITE LIKELIHOOD METHODS , 2011 .

[16]  Christian Julliard,et al.  Consumption Risk and the Cross Section of Expected Returns , 2004, Journal of Political Economy.

[17]  Larry G. Epstein,et al.  Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis , 1991, Journal of Political Economy.

[18]  Philippe Rigollet,et al.  Kullback-Leibler aggregation and misspecified generalized linear models , 2009, 0911.2919.

[19]  Ravi Jagannathan,et al.  Assessing Specification Errors in Stochastic Discount Factor Models , 1994 .

[20]  Raymond Kan,et al.  Spurious Inference in Reduced‐Rank Asset‐Pricing Models , 2017 .

[21]  Z. Cai,et al.  PRICING KERNEL ESTIMATION: A LOCAL ESTIMATING EQUATION APPROACH , 2015, Econometric Theory.

[22]  Yuhong Yang.  Mixing Strategies for Density Estimation , 2000 .

[23]  C. Varin.  On composite marginal likelihoods , 2008 .

[24]  Michael J. Stutzer,et al.  A Bayesian approach to diagnosis of asset pricing models , 1995 .

[25]  A. Tsybakov,et al.  Sparse Estimation by Exponential Weighting , 2011, 1108.5116.

[26]  Francis X. Diebold.  A Note on Bayesian Forecast Combination Procedures , 1991 .

[27]  E. Maasoumi,et al.  A Dependence Metric for Possibly Nonlinear Processes , 2004 .

[28]  E. Maasoumi.  How to live with misspecification if you must , 1990 .

[29]  L. Birge,et al.  Model selection via testing: an alternative to (penalized) maximum likelihood estimators , 2006 .

[30]  E. Maasoumi.  The Measurement and Decomposition of Multi-dimensional Inequality , 1986 .

[31]  Motohiro Yogo,et al.  The Rodney L. White Center for Financial Research a Consumption-based Explanation of Expected Stock Returns , 2022 .

[32]  E. Maasoumi.  A Modified Stein-like Estimator for the Reduced Form Coefficients of Simultaneous Equations , 1978 .

[33]  K. McConway.  Marginalization and Linear Opinion Pools , 1981 .

[34]  V. Chernozhukov,et al.  An MCMC Approach to Classical Estimation , 2002, 2301.07782.

[35]  E. Maasoumi.  A compendium to information theory in economics and econometrics , 1993 .

[36]  René Garcia,et al.  Assessing Misspecified Asset Pricing Models with Empirical Likelihood Estimators , 2009 .

[37]  Jeffrey S. Racine,et al.  Entropy and predictability of stock market returns , 2002 .

[38]  Anish Ghosh,et al.  What is the Consumption-CAPM Missing? An Information-Theoretic Framework for the Analysis of Asset Pricing Models , 2011 .