Geodesic
Estimation and bimodality testing in the cusp model
Kybernetika, Tome 54 (2018) no. 4, pp. 798-814
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The probability density function of the stochastic cusp model belongs to the class of generalized exponential distributions. It accommodates variable skewness, kurtosis, and bimodality. A statistical test for bimodality of the stochastic cusp model using the maximum likelihood estimation and delta method for Cardan's discriminant is introduced in this paper, as is a necessary condition for bimodality, which can be used for simplified testing to reject bimodality. Numerical maximum likelihood estimation of the cusp model is simplified by analytical reduction of the parameter space dimension, and connection to the method of moment estimates is shown. A simulation study is used to determine the size and power of the proposed tests and to compare pertinence among different tests for various parameter settings.
The probability density function of the stochastic cusp model belongs to the class of generalized exponential distributions. It accommodates variable skewness, kurtosis, and bimodality. A statistical test for bimodality of the stochastic cusp model using the maximum likelihood estimation and delta method for Cardan's discriminant is introduced in this paper, as is a necessary condition for bimodality, which can be used for simplified testing to reject bimodality. Numerical maximum likelihood estimation of the cusp model is simplified by analytical reduction of the parameter space dimension, and connection to the method of moment estimates is shown. A simulation study is used to determine the size and power of the proposed tests and to compare pertinence among different tests for various parameter settings.
DOI : 10.14736/kyb-2018-4-0798
Classification : 62F03
Keywords: multimodal distributions; cusp model; bimodality test; reduced maximum likelihood estimation 
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Voříšek, Jan. Estimation and bimodality testing in the cusp model. Kybernetika, Tome 54 (2018) no. 4, pp. 798-814. doi: 10.14736/kyb-2018-4-0798

[1] Arnold, V. I.: Catastrophe Theory. Springer-Verlag, Berlin 1992. | DOI | MR

[2] Barunik, J., Kukačka, J.: Realizing stock market crashes: stochastic cusp catastrophe model of returns under time-varying volatility. Quantitative Finance 15 (2015), 959-973. | DOI | MR

[3] Barunik, J., Vošvrda, M.: Can a stochastic cusp catastrophe model explain stock market crashes?. J. Economic Dynamics Control 33 (2009), 1824-1836. | DOI | MR

[4] Cobb, L.: Stochastic catastrophe models and multimodal distributions. Behavioral Sci. 23 (1978), 360-374. | DOI | MR

[5] Cobb, L., Watson, B.: Statistical catastrophe theory: An overview. Math. Modell. 1 (1980), 311-317. | DOI | MR

[6] Cobb, L.: Parameter estimation for the cusp catastrophe model. Behavioral Sci. 26 (1981), 75-78. | DOI

[7] Cobb, L., Koppstein, P., Chen, N. H.: Estimation and moment recursion relations for multimodal distributions of the exponential family. J. Amer. Statist. Assoc. 78 (1983), 124-130. | DOI | MR

[8] Creedy, J., Lye, J., Martin, V.: A non-linear model of the real US/UK exchange rate. Econom. Modell. 11 (1996), 669-686. | DOI

[9] Diks, C., Wang, J.: Can a stochastic cusp catastrophe model explain housing market crashes?. J. Econom. Dynamics Control 69 (2016), 68-88. | DOI

[10] Fernandes, M.: Financial crashes as endogenous jumps: estimation, testing and forecasting. J. Econom. Dynamics Control 30 (2006), 111-141. | DOI | MR

[11] Grasman, R. P. P. P., Maas, H. L. J. van der, Wagenmakers, E. J.: Fitting the cusp catastrophe in R: A cusp package primer. J. Statist. Software 32 (2009), 1-28. | DOI

[12] Hartigan, J. A., Hartigan, P. M.: The dip test of unimodality. Ann. Statist. 13 (1985), 70-84. | DOI | MR

[13] Kodde, D. A., Palm, F. C.: Wald criteria for jointly testing equality and inequality restrictions. Econometrica 54 (1986), 1243-1248. | DOI | MR

[14] Koh, S. K., Fong, W. M., Chan, F.: A Cardans discriminant approach to predicting currency crashes. J. Int. Money Finance 26 (2007), 131-148. | DOI

[15] Lehman, E. L., Romano, J. P.: Testing Statistical Hypotheses. Third edition. Springer-Verlag, New York 2005. | DOI | MR

[16] Matz, A. W.: Maximum likelihood parameter estimation for the quartic exponential distribution. Technometrics 20 (1978), 475-484. | DOI

[17] Thom, R.: Structural Stability and Morpohogenesis. W. A. Benjamin, New York 1975. | MR

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