Duzgunlestirilmis Fonksiyonel Ana Bilesenler Analizi Ile Imkb Verilerinin Incelenmesi

In most situations, modern technological developments give rise to the cases where samples are drawn from a population of real random functions. Functional Data Analysis (FDA) is an appropriate multivariate statistical approximation since the classical multivariate methods can not be used when a random sample consists of such n-real functions. Generally the functions are sampled discretely in time and a certain smoothing technique is used to obtain underlying functions. In this study we first give a detailed theory of B-Splines and then obtain cubic splines as linear combinations based on the coefficients resulted from an implementation of the Roughness Penalty Method. We then present a comprehensive theoretical background of the functional data analysis with a special attention given to the functional and regularized functional principal components concepts that are very useful to explore and interpret the variability of the functions and also their derivatives especially when one has a large number of functions. Finally, an application of the regularized functional principal components on the weekly closing share prices data of the thirteen companies belonging to the ISE-100 index is presented. Interpretations of the derivative functions, covariance surface and principal component functions are also given in detail.