Functional Data Analysis - An application to weather data

Abstract

The goal of this project is to introduce the topic of Functional Data Analysis (FDA) a relative new research area that resembles and puts together different fields and sectors, such as Statistics, Econometrics, Machine Learning, ... Actually, it can be considered a branch of Statistics. Functional Data Analysis was developed in order to address some data analysis problem, especially for what concerns phenomena that show, by nature, a relative ”smooth” behavior, i.e. that can be represented by curves that present some sort of regularity, and that varies over a continuum. My work has been articulated in the following manner: the first Chapter (1) is dedicated to the main and must-known theory necessary for understanding what FDA is and what kind of works can be devised using its particular techniques. Chapter 2 presents the data that are deployed in carrying out my empirical analysis and in particular: the type of data with all their characteristics, the preliminary analysis through which data has been processed in order to clean and finalize them. The third Chapter (3) contains the empirical analysis and includes all the graphs and plots that are helpful to understand the results achieved. Finally, Chapter 4 is devoted to conclusion and remarks and provide hints for developing further the work. As for the empirical part, I have focused my attention on weather and climate and in particular on daily temperature and precipitation amounts related to 30 different weather stations in Europe. As for the code part, nowadays many packages or toolboxes for different languages (R, MATLAB, python) have been devised by practitioners aiming to address all the complexity of functional data analysis. In my application, I have opted for using MATLAB and in particular the FDA Toolbox.