|Location||Call number||Copy number||Status||Date due|
|Sala B : Armadio Tesi||THS_2015 332 A123 (Browse shelf)||1||Available|
Tesi di diploma di 1° livello per la Classe delle Scienze Sperimentali Diploma di 1° livello Scuola Superiore di Catania, Catania, Italy 2015 A.A. 2014/2015 Sul front.: A.A. 2015/2016
Includes bibliographical references (p. 61-64).
Tesi discussa il 15/12/2015.
Financial markets behave as complex systems that need a statistical analysis; one of their main features is that they reveal strong dependences between the price movements of the companies' stocks. The way the stocks depend on each other, together with a network representation of the market, can be revealed through partial correlation matrices constructed using the time series of the stocks' price returns. Nevertheless, the presence of statistical noise in data requires the application of some estimators able to select the non-zero entries of the partial correlation matrix. LASSO estimation and its algorithms for partial correlation matrices (SPACE) are studied in this thesis. In particular, after a brief theoretical introduction to the problem, we present the results obtained by using one-factor and multi-factor models in order to simulate data whose noiseless partial correlations and general features are known. Comparisons between partial correlation matrices estimated applying LASSO method to these data and noiseless matrices have been performed. They reveal that these matrices are more similar when the number of variables and the length of the time series are larger. Moreover, making the variances of the variables uniform turns out to be a necessary condition for the application of the method, since these variances influence the filtering process. We also discover the emergence of critical behaviours in the study of the probability of having a link. In one-factor models, links are rejected whenever the product of the coefficients which relate the variables to the principal factor is under a specific threshold. Even studying the topology of the network, critical trends appear, since the dimensions of clusters change abruptly beyond certain values of these coefficients. Finally, we present an application to real financial time series. In this case, we test the goodness of a one-factor model approximation, comparing results with the ones extracted from simulations. Knowing the industry sectors classification of the companies studied, we prove the efficiency of partial correlation estimations about the detection of clusters, showing that it is better when the effect of the principal factor is removed
from data. Lastly, we consider short time windows and perform a dynamical analysis, providing brief conclusions.