Analyzing skewed financial data using skew scale-shap mixtures of multivariate normal distributions

[1] Adcock, C., Eling, M., & Loper do, N. (2015) Skewed distributions in  -nance and actuarial science: a review. Europian Journal of Finance 21:1{29. https://doi.org/10.1080/1351847X.2012.720269

[2] Amiri, M., & Balakrishnan, N. (2022). Hessian and increasing-Hessian orderings of scale-shape mixtures of multivariate skew-normal distributions and applications. Journal of Computational and Applied Mathematics, 402, 113801.
https://doi.org/10.1016/j.cam.2021.113801

[3] Arellano-Valle, R. B., & Genton, M. G. (2005). On fundamental skew distributions. Journal of Multivariate Analysis, 96(1), 93-116. https://doi.org/10.1016/j.jmva.2004.10.002

[4] Azzalini, A., & Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press.

[5] Bodie, Z., & Kane, A. (2020). Essentials of investments.

[6] Branco, M.D., & Dey, D. k. (2001). A general class of multivariate skew-elliptical distributions. Journal of Multivariate Analysis, 79, 99{113. https://doi.org/10.1006/jmva.2000.1960

[7] Cont, R. (2007). Volatility clustering in  nancial markets: empirical facts and agentbased models. In Long memory in economics (pp. 289-309). Berlin, Heidelberg: Springer Berlin Heidelberg.

[8] Denkowska, A., & Wanat, S. (2020). A tail dependence-based MST and their topological indicators in modeling systemic risk in the European insurance sector. Risks, 8(2), 39. https://doi.org/10.3390/risks8020039

[9] Fabozzi, F. J., Markowitz, H. M., & Gupta, F. (2008). Portfolio selection. Handbook of  nance.

[10] Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of  nancial economics, 33(1), 3-56. https://doi.org/10.1016/0304-405X(93)90023-5

[11] Ferreira, C. S., Bolfarine, H., & Lachos, V. H. (2011). Skew scale mixtures of normal distributions: properties and estimation. Statistical Methodology, 8(2), 154-171. https://doi.org/10.1016/j.stamet.2010.09.001

[12] Ferreira, C. S., Lachos, V. H., & Bolfarine, H. (2016). Likelihood-based inference for multivariate skew scale mixtures of normal distributions. AStA Advances in Statistical Analysis, 100(4), 421-441. https://doi.org/10.1007/s10182-016-0266-z

[13] Gomez-Deniz, E., Caldern-Ojeda, E., & Gomez, H. W. (2022). Symmetric and Asymmetric Distributions: Theoretical Developments and Applications III. Symmetry, 14(10), 21-43. https://doi.org/10.3390/sym14102143

[14] Hardle, W. K., & Simar, L. (2019). Applied multivariate statistical analysis. Springer Nature.

[15] Harvey, C. R., & Siddique, A. (2000). Conditional skewness in asset pricing tests. The Journal of  nance, 55(3), 1263-1295. https://doi.org/10.1111/0022-1082.00247

[16] Jamalizadeh, A., & Lin, T. I. (2017). A general class of scale-shape mixtures of skewnormal distributions: properties and estimation. Computational Statistics, 32, 451-474. https://doi.org/10.1007/s00180-016-0691-1

[17] Jorion, P. (2007). Value at risk: the new benchmark for managing  nancial risk. McGraw-Hill.

[18] Junior, L. S., & Franca, I. D. P. (2012). Correlation of  nancial markets in times of crisis. Physica A: Statistical Mechanics and its Applications, 391(1-2), 187-208. https://doi.org/10.1016/j.physa.2011.07.023

[19] Kotz, S., Balakrishnan, N., & Johnson, N. L. (2004). Continuous multivariate distributions, Volume 1: Models and applications (Vol. 1). John Wiley & Sons.

[20] Liu, C.H., & Rubin, D.B. (1994). The ECME algorithm: a simple extension of EM and ECM with faster monotone convergence. Biometrika, 81, 633{648. https://doi.org/10.1093/biomet/81.4.633

[21] Madan, D. B. (2020). Multivariate distributions for  nancial returns. International Journal of Theoretical and Applied Finance, 23(06), 2050041. https://doi.org/10.1142/S0219024920500417

[22] Mahdavi, A., Amirzadeh, V., Jamalizadeh, A., & Lin, T. I. (2021). A Multivariate exible skew-symmetric-normal distribution: Scale-shape mixtures and parameter estimation via selection representation. Symmetry, 13(8), 1343.
https://doi.org/10.3390/sym13081343

[23] Mardia, K. V., Kent, J. T., & Bibby, J. M. (1979). Multivariate Analysis. Academic Press.

[24] Mata, L. M., Nu~nez Mora, J. A., & Serrano Bautista, R. (2021). Multivariate Distribution in the Stock Markets of Brazil, Russia, India, and China. SAGE Open, 11(2), 21582440211009509. https://doi.org/10.1177/21582440211009509

[25] McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative risk management: Concepts, techniques and tools. Princeton university press.

[26] Meng, X. L.,& Rubin, D. B. (1993). Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika, 80, 267-278. https://doi.org/10.1093/biomet/80.2.267

[27] Mondal, S., Arellano-Valle, R. B., & Genton, M. G. (2023). A multivariate modi ed skew-normal distribution. Statistical Papers, 1-45. https://doi.org/10.1007/s00362-023-01397-1

[28] Naderi, M., Arabpour, A., & Jamalizadeh, A. (2018). Multivariate normal mean-variance mixture distribution based on Lindley distribution. Communications in Statistics-Simulation and Computation, 47, 1179{1192. https://doi.org/10.1080/03610918.2017.1307400

[29] Pourmousa, R., Jamalizadeh, A., & Rezapour, M. (2015). Multivariate normal mean{variance mixture distribution based on Birnbaum{Saunders distribution. Journal of Statistical Computation and Simulation, 85(13), 2736{2749. https://doi.org/10.1080/00949655.2014.937435

[30] Pu, T., Zhang, Y., & Yin, C. (2023). Generalized location-scale mixtures of elliptical distributions: De nitions and stochastic comparisons. Communications in Statistics-Theory and Methods, 1-25. https://doi.org/10.1080/03610926.2023.2165407