In this paper, we used the Singular Value Decomposition (SVD) to find the relationships in the fluctuation of the six market indexes CAC 40, DAX, DOW JONES 30, FTSE 100, IBEX35 and NIKKEI 225 during the year 2018. This technique allows relating several indexes in a very similar way the classical Principal Component Analysis (PCA). In fact, we will just use the statistical software to confirm some results.
References
[1]
Bulirsch, R. and Stoer, J. (1980) Introduction to Numerical Analysis. Springer, Berlin.
[2]
Golub, G.H. and Van Loan, C.F. (1989) Matrix Computations. The Johns Hopkins University Press, Baltimore.
[3]
Walkins, D.S. (1991) Fundamentals of Matrix Computations. John Wiley, Hoboken.
[4]
Higham, N.J. (1996) Accuracy and Stability of Numerical Algorithms. SIAM, Philadelphia.
[5]
Trefethen, L.N. and Bau, D. (1997) Numerical Linear Algebra. SIAM, Philadelphia. https://doi.org/10.1137/1.9780898719574
[6]
Meyer, C.D. (2000) Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia. https://doi.org/10.1137/1.9780898719512
[7]
Moler, C.B. (2004) Numerical Computing with Matlab. SIAM, Philadelphia. https://doi.org/10.1137/1.9780898717952
[8]
Yang, W.Y., Cao, W., Chung, T.S. and Morris, J. (2005) Applied Numerical Methods Using Matlab. Wiley Interscience, Hoboken. https://doi.org/10.1002/0471705195
[9]
Ascher, U.M. and Greif, C. (2011) A Firts Course in Numerical Methods. SIAM, Philadelphia. https://doi.org/10.1137/9780898719987
[10]
Holmes, M.H. (2016) Introduction to Scientific Computing and Data Analysis. Springer, Berlin. https://doi.org/10.1007/978-3-319-30256-0
[11]
Marques de Sa, J.P. (2007) Applied Statistics Using SPSS, STATISTICA, MATLAB and R. Second Edition, Springer, Berlin. https://doi.org/10.1007/978-3-540-71972-4
[12]
Jolliffe, I.T. (2010) Principal Component Analysis. Second Edition, Springer, Berlin. https://doi.org/10.1007/978-3-642-04898-2_455
[13]
Abdi, H. and Williams, L.J. (2010) Principal Component Analysis. Wiley Interdisciplinary Reviews: Computational Statistics, 2, 433-459. https://doi.org/10.1002/wics.101
[14]
Rencher, A.C. and Christensen, W.F. (2012) Methods of Multivariate Analysis. 3rd Edition, Wiley, Hoboken. https://doi.org/10.1002/9781118391686
[15]
Dolliffe, I.T. (2016) Computational and Statistical Methods for Analysing Big Data with Applications. Elsevier, Amsterdam.
[16]
Chalfileld, C. and Collins, A.J. (2017) Introduction to Multivariate Analysis. Chapman and Hall/CRC, London.
Husson, F., Lê, S. and Pag, J. (2017) Exploring Multivariate Analysis by Examples Using R. CRC Press, Boca Raton. https://doi.org/10.1201/b21874
[19]
Peres-Neto, P.R., Jackson, D.A. and Somers, K.M. (2005) How Many Principal Components? Stopping Rules for Determining the Number of Non-Trivial Axes Revisited. Computational Statistic & Data Analysis, 49, 974-997. https://doi.org/10.1016/j.csda.2004.06.015
[20]
Josse, J. and Husson, F. (2012) Selecting the Number of Components in Principal Component Analysis Using Cross-Validation Approximations. Computational Statistic & Data Analysis, 56, 1869-1879. https://doi.org/10.1016/j.csda.2011.11.012
[21]
Harari, Y.N. (2018) 21 Lessons for the 21st Century. Vintage Books, New York. https://doi.org/10.17104/9783406727795-21
