Improvement of TestH: a C Library for Generating Self-Similar Series and for Estimating the Hurst Parameter

• Autor(a) principal: Ramos, Cristiano Duarte Gonçalves
• Data de Publicação: 2017
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Texto Completo: http://hdl.handle.net/10400.6/7836
• topic: Auto-Semelhança; Dependência de Longo Alcance; Estimadores do Parâmetro de Hurst; Geradores de Sequências Auto-Semelhantes; Movimento Browniano Fracionário; Passeio Aleatório; Ruído Gaussiano Fracionário; Testh

The discovery of consistent dependencies between values in certain data series paved the way for the development of algorithms that could, somehow, classify the degree of self-similarity between values and derive considerations about the behavior of these series. This self-similarity metric is typically known as the Hurst Parameter, and allows the classification of the behavior of a data series as persistent, anti-persistent, or purely random. This discovery was highly relevant in the field of computer networks, inclusively helping companies to develop equipment and infrastructure that suit their needs more efficiently. The Hurst Parameter is relevant in many other fields, and it has been for exemple applied in the study of geologic phenomena [KTC07] or even on areas related with health sciencies[VAJ08, HPS+12]. There are several algorithms for estimating the Hurst Parameter [Hur51, Hig88, RPGC06], and each one of them has its strengths and weaknesses. The usage of these algorithms is sometimes difficult, motivating the creation of tools or libraries that provide them in a more user-friendly manner. Unfortunately, and despite of being an area that has been studied for decades, the tools available have limitations and do not implement all algorithms available in the literature. The work presented in this dissertation consists on the improvement of TestH, a library written in ANSI C for the study of self-similarity in time series, which was initially developed by Fernandes et al. [FNS+14]. These improvements are materialized as the addition of algorithms to estimate the Hurst Parameter and to generate self-similar sequences. Additionally, auxiliary functions were implemented, along with code refactoring, documentation of the application programming interface and the creation of a website for the project. This dissertation is mostly focused on the algorithms that were introduced in TestH, namely the Periodogram, the Higuchi method, the Hurst Exponent by Autocorrelation Function and the Detrended Fluctuation Analysis estimators, and the Davies and Hart method for generating selfsimilar sequences. In order to turn TestH into a robust and trustable library, several tests were performed comparing the results of these implementations with the values provided by similar tools. The overall results obtained in these tests are in line with expectations and the algorithms that are simultaneously implemented in TestH and in the other tools analyzed (for example, the Periodogram) returned very similar results, corroborating the belief that the methods were well implemented.