×

zbMATH — the first resource for mathematics

Chi-squared tests for evaluation and comparison of asset pricing models. (English) Zbl 1443.62451
Summary: This paper presents a general statistical framework for estimation, testing and comparison of asset pricing models using the unconstrained distance measure of L. P. Hansen and R. Jagannathan [“Assessing specification errors in stochastic discount factor models”, J. Finance 52, No. 2, 557–590 (1997; doi:10.1111/j.1540-6261.1997.tb04813.x)]. The limiting results cover both linear and nonlinear models that could be correctly specified or misspecified. We propose modified versions of the existing model selection tests and new pivotal specification and model comparison tests with improved finite-sample properties. In addition, we provide formal tests of multiple model comparison. The excellent size and power properties of the proposed tests are demonstrated using simulated data from linear and nonlinear asset pricing models.

MSC:
62P20 Applications of statistics to economics
Software:
nlmdl
PDF BibTeX XML Cite
Full Text: DOI Link
References:
[1] Abel, A., Asset prices under habit formation and catching up with the joneses, American Economic Review, 80, 38-42, (1990)
[2] Ahn, S. C.; Gadarowski, C., Small sample properties of the GMM specification test based on the hansen – jagannathan distance, Journal of Empirical Finance, 11, 109-132, (2004)
[3] Almeida, C.; Garcia, R., Assessing misspecified asset pricing models with empirical likelihood estimators, Journal of Econometrics, 170, 519-537, (2012) · Zbl 1443.62419
[4] Andrews, D. W.K., An introduction to econometric applications of empirical process theory for dependent random variables, Econometric Reviews, 12, 183-216, (1993) · Zbl 0802.62099
[5] Andrews, D. W.K., Empirical process methods in econometrics, (Engle, R. F.; McFadden, D. L., Handbook of Econometrics, (1994), North-Holland Amsterdam), 2247-2294
[6] Andrews, D. W.K.; Soares, G., Inference for parameters defined by moment inequalities using generalized moment selection, Econometrica, 78, 119-158, (2010) · Zbl 1185.62040
[7] Brown, D. P.; Gibbons, M., A simple econometric approach for utility-based asset pricing models, Journal of Finance, 40, 359-381, (1985)
[8] Chen, X.; Hong, H.; Shum, M., Nonparametric likelihood ratio model selection tests between parametric likelihood and moment condition models, Journal of Econometrics, 141, 109-140, (2007) · Zbl 1418.62426
[9] Chen, X.; Ludvigson, S. C., Land of addicts? an empirical investigation of habit-based asset pricing models, Journal of Applied Econometrics, 24, 1057-1093, (2009)
[10] Childs, D. R., Reduction of the multivariate normal integral to characteristic form, Biometrika, 54, 293-300, (1967) · Zbl 0178.22205
[11] Cochrane, J. H., Asset pricing, (2005), Princeton University Press Princeton
[12] Fama, E. F.; French, K. R., Common risk factors in the returns on stocks and bonds, Journal of Financial Economics, 33, 3-56, (1993) · Zbl 1131.91335
[13] Gallant, R. A., Nonlinear statistical models, (1987), Wiley New York · Zbl 0611.62071
[14] Golden, R. M., Discrepancy risk model selection test theory for comparing possibly misspecified or nonnested models, Psychometrika, 68, 229-249, (2003) · Zbl 1306.62417
[15] Gospodinov, N., Kan, R., Robotti, C., 2011. On the Hansen-Jagannathan distance with a no-arbitrage constraint. Discussion Paper. Federal Reserve Bank of Atlanta.
[16] Gospodinov, N.; Kan, R.; Robotti, C., Further results on the limiting distribution of GMM sample moment conditions, Journal of Business and Economic Statistics, 30, 494-504, (2012)
[17] Hall, A. R.; Pelletier, D., Nonnested testing in models estimated via generalized method of moments, Econometric Theory, 27, 443-456, (2011) · Zbl 1210.62240
[18] Hansen, P. R., A test for superior predictive ability, Journal of Business and Economic Statistics, 23, 365-380, (2005)
[19] Hansen, L. P.; Heaton, J. C.; Luttmer, E. G.J., Econometric evaluation of asset pricing models, Review of Financial Studies, 8, 237-274, (1995)
[20] Hansen, L. P.; Jagannathan, R., Assessing specification errors in stochastic discount factor models, Journal of Finance, 52, 557-590, (1997)
[21] Imbens, G. W.; Spady, R. H.; Johnson, P., Information theoretic approaches to inference in moment condition models, Econometrica, 66, 333-357, (1998) · Zbl 1055.62512
[22] Jagannathan, R.; Wang, Z., The conditional CAPM and the cross-section of expected returns, Journal of Finance, 51, 3-53, (1996)
[23] Kan, R.; Robotti, C., Specification tests of asset pricing models using excess returns, Journal of Empirical Finance, 15, 816-838, (2008)
[24] Kan, R.; Robotti, C., Model comparison using the hansen – jagannathan distance, Review of Financial Studies, 22, 3449-3490, (2009)
[25] Kan, R., Robotti, C., Shanken, J., 2012. Pricing model performance and the two-pass cross-sectional regression methodology. Journal of Finance (forthcoming).
[26] Kan, R.; Zhang, C., GMM tests of stochastic discount factor models with useless factors, Journal of Financial Economics, 54, 103-127, (1999)
[27] Kitamura, Y., 2000. Comparing misspecified dynamic econometric models using nonparametric likelihood. Working Paper. University of Pennsylvania.
[28] Kudo, A., A multivariate analogue of the one-sided test, Biometrika, 50, 403-418, (1963) · Zbl 0121.13906
[29] Lettau, M.; Ludvigson, S. C., Resurrecting the (C)CAPM: A cross-sectional test when risk premia are time-varying, Journal of Political Economy, 109, 1238-1287, (2001)
[30] Li, H.; Xu, Y.; Zhang, X., Evaluating asset pricing models using the second hansen – jagannathan distance, Journal of Financial Economics, 97, 279-301, (2010)
[31] Lien, D.; Vuong, Q. H., Selecting the best linear regression model: a classical approach, Journal of Econometrics, 35, 3-23, (1987) · Zbl 0629.62062
[32] Marcellino, M.; Rossi, B., Model selection for nested and overlapping nonlinear, dynamic and possibly mis-specified models, Oxford Bulletin of Economics and Statistics, 70, 867-893, (2008)
[33] Nagel, S.; Singleton, K. J., Estimation and evaluation of conditional asset pricing models, Journal of Finance, 66, 873-909, (2011)
[34] Newey, W. K., Generalized method of moments specification testing, Journal of Econometrics, 29, 229-256, (1985) · Zbl 0606.62132
[35] Newey, W. K.; West, K. D., A simple positive semi-definite heteroskedasticity and autocorrelation consistent covariance matrix estimator, Econometrica, 55, 703-708, (1987) · Zbl 0658.62139
[36] Parker, J. A.; Julliard, C., Consumption risk and the cross section of expected returns, Journal of Political Economy, 113, 185-222, (2005)
[37] Pollard, D., A central limit theorem for \(k\)-means clustering, Annals of Probability, 10, 919-926, (1982) · Zbl 0502.62055
[38] Rivers, D.; Vuong, Q. H., Model selection tests for nonlinear dynamic models, Econometrics Journal, 5, 1-39, (2002) · Zbl 1010.62110
[39] Smith, R. J., Alternative semi-parametric likelihood approaches to generalized method of moments estimation, Economic Journal, 107, 503-519, (1997)
[40] Sowell, F. B., Optimal tests for parameter instability in the generalized method of moments framework, Econometrica, 64, 1085-1107, (1996) · Zbl 0859.62060
[41] Stock, J. H.; Wright, J. H., GMM with weak identification, Econometrica, 68, 1055-1096, (2000) · Zbl 1015.62105
[42] Sun, H., A general reduction method for \(n\)-variate normal orthant probability, Communications in Statistics - Theory and Methods, 11, 3913-3921, (1988) · Zbl 0696.62055
[43] Sun, H., A Fortran subroutine for computing normal orthant probabilities of dimensions up to nine, Communications in Statistics - Simulation and Computation, 17, 1097-1111, (1988) · Zbl 0695.62001
[44] Vuong, Q. H., Likelihood ratio tests for model selection and non-nested hypotheses, Econometrica, 57, 307-333, (1989) · Zbl 0701.62106
[45] White, H., A reality check for data snooping, Econometrica, 68, 1097-1126, (2000) · Zbl 1008.62116
[46] Wolak, F. A., An exact test for multiple inequality and equality constraints in the linear regression model, Journal of the American Statistical Association, 82, 782-793, (1987) · Zbl 0633.62051
[47] Wolak, F. A., Testing inequality constraints in linear econometric models, Journal of Econometrics, 31, 205-235, (1989) · Zbl 0678.62103
[48] Yogo, M., A consumption-based explanation of expected stock returns, Journal of Finance, 61, 539-580, (2006)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.