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.Functional Data Analysis, Functional Principal Component Analysis, Regularized Functional Principal Component Analysis, Smoothing, Roughness Penalty Approach, Cubic Spline, Eigenvalue-Eigenfunction Decomposition, Dimension Reduction

Functional Cluster and Canonical Correlation Analysis of EU Countries by Number of Daily Deaths and Stringency Index During Covid-19 Pandemic

The danger of a global pandemic, such as the new Coronavirus (Covid-19),is obvious. This study aims to investigate the behavior and relationship of thenumber of daily new conrmed deaths per million and the stringency indexof twenty-seven European Union (EU) countries by utilizing functional clusteranalysis and functional canonical correlation analysis. Functional clusteranalysis was used to observe how countries cluster together according to dailydeaths during the time interval between March and July 2020. Functionalcanonical correlation analysis was also utilized to measure the correlationbetween the frequency index and daily deaths, and also to determine therelative positions of countries concerning their respective variability structure.The data is obtained from OWID. Here, it is seen that Italy, Spain,Belgium, and France are particularly aected by the pandemic during thetime interval within the EU countries, and the course of daily deaths is in adierent position compared to other EU countries. At the same time, a veryhigh relationship emerged between the stringency index and daily deaths asexpected

Karsilastirmali Olarak Fonksiyonel Ana Bilesenler Analizi ve GSYIH Verilerinin Incelenmesi

Bu calismada oncelikle Ana Bilesenler ve Fonksiyonel Ana Bilesenler Analizi karsilastirmali olarak ele alinmis ve ekonomik gelismenin bir gostergesi olan Gayri Safi Yurt Ici Hasila (GSYIH) verileri Fonksiyonel Ana Bilesenler Analizi ile incelenerek verileri fonksiyonel acidan ele almanin avantajlari sunulmustur. Fonksiyonel Ana Bilesenler Analizi ile 1987-2001 yillari arasinda ulkemizdeki 7 bolgenin GSYIH verilerinin degiskenlik yapisi %99 gibi cok yuksek bir varyans aciklama yuzdesine sahip birinci ana bilesen fonksiyonuyla ortaya konulmustur. Bu ana bilesen fonksiyonun yardimiyla GSYIH acisindan bolgeler arasindaki degiskenligin 1996 yilindan sonra bir artisa gectigi, ancak 2000 yilinin ortalarindan sonra da tekrar azalmaya basladigi tespit edilmistir.

Smoothed functional canonical correlation analysis of humidity and temperature data

<div><p>This paper focuses on smoothed functional canonical correlation analysis (SFCCA) to investigate the relationships and changes in large, seasonal and long-term data sets. The aim of this study is to introduce a guideline for SFCCA for functional data and to give some insights on the fine tuning of the methodology for long-term periodical data. The guidelines are applied on temperature and humidity data for 11 years between 2000 and 2010 and the results are interpreted. Seasonal changes or periodical shifts are visually studied by yearly comparisons. The effects of the ‘number of basis functions’ and the ‘selection of smoothing parameter’ on the general variability structure and on correlations between the curves are examined. It is concluded that the number of time points (knots), number of basis functions and the time span of evaluation (monthly, daily, etc.) should all be chosen harmoniously. It is found that changing the smoothing parameter does not have a significant effect on the structure of curves and correlations. The number of basis functions is found to be the main effector on both individual and correlation weight functions.</p></div