Discovering and Modeling the Driving Forces of Multidimensional Scales with Application to Financial Data
Keywords:
Descriptive tools, Gaussian distribution, Spectral decomposition, Dimension reduction, Driving Forces, principal components, modeling characteristics, skewness and kurtosis, Financial FactorsAbstract
In this paper, the driving forces are represented by linear and nonlinear principal components. In order to extract such forces, dimension reduction is applied using spectral decomposition technique. The most contributing lower order principal components are retained to represent the driving forces. The modeling of these forces is achieved in comparison to the Gaussian one.
References
Freund, J. (1992). Mathematical Statistics. Fifth Edition, Prentice-Hall, New Jersy.
Reiss, R.-D. and Thomas, M. (2007). Statistical Analysis of Extreme values with Applications to Insurance, Finance, Hydrology and other Fields . Birkhaeuser, Berlin.
Johnson, N., and Wichern, D. (1988). Applied Multivariate Statistical Analysis. Second Edition, Printice-Hall Interntional, New Jersy.
Timm, N. H. (2002). Applied Multivariate Analysis. Springer-Verlag, Berlin.
Franc, V. and Hlavac, V. (2004). Statistical Pattern Recognition Toolbox for Matlab, User’s Guide. Technical University Prague.
Mardia, K. V. (1970). Measures of Multivariate Skewness and Kurtosis with Applications.
Biometrika, 57(3):519-530.
Rosipal, R., Trejo, J. and Cichock, A. (2000). Kernel Principal Components Regression with EM Approach to Nonlinear Principal Components Extraction. Technical Report. University of Paisley, Scotland.
Cangelsoni, R. and Goriely, A. (2007). Component retention in Principal component Analysis with Application to cDNA microarray data. Biology Direct, 2:2, BioMed Central.
Falk, M., Marohn, F., and Tewes, B. (2002). Foundation of Statistical Analysis and Applications with SAS. First Edition, Birkhaeuser, Berlin.
Hastie, T., Tibshirani, R. and Friedman, J. (2011). The Elements of Statistical Learning: Data Mining, Inference and Prediction. Third Edition, Springer, Berlin.
Seber, G. A. F. (2004). Multivariate Observations. John Wiley & Sons, New York.
