Improving time series modeling by decomposing and analysing stochastic and deterministic influences

Abstract

First of all, I would like to offer my gratitude to God, who has been blessing me every single day. I also wish to express my sincere gratitude to my advisor, professor Rodrigo Mello. During the last years, he was more than a formal advisor, helping me to understand new concepts and working hard to produce this work. Thank you very much, Rodrigo, for showing me the importance of researching without having numbers as parameter. For sure, our collaboration and friendship will never end. Well, I was impatient to start talking about my wife and my daughter. Tati, you are my strength, my motivation, and my inspiration. Thank you very much for your patience and love. You are present in every page of this thesis. Thank you very much for making my days and trips funnier. Mari, my little girl, you came up a few months ago, but I cannot even remeber my life before you. You suddenly became the main reason for everything. Your tender smile moves me and makes me forget any tough situation. I am deeply grateful to my father Robério, my mother Josinha, my brothers Guga, Joyce (Guga's wife and my stepsister :]), and Bebel. You are the greatest models for me. I am pretty sure you are always by my side, regardless the situation I know I can count on you. I love you so much. My grandfather Alcides and my grandmother Isabel, you started all this mess when you left behind a quiet life in the countryside to live in a bigger city and give better conditions to your children. I am forever grateful to you. I would like to thank my new family Valdeci, Dilzete, Tiago, Eva e Rodrigo for being always there sharing amazing moments. Professor Michall Small, thank you very much for your help and support during my stay in Hong Kong. You allowed me to develop a new research line and to try out one of the most incredible experience of my life. The memories from HK will never leave my head. Thank you also Ruoxi Xiang, Xiaoke Xu, and Liu Xiaofan for our chats that helped me during the adaptation process and made me to learn and respect your culture even more. I also thank Professor Lael Parrott for your help while I was in Montreal, for your dedi ication during our meetings and all support after my return to Brazil. I am also thankful to Gillaume Latombe, Phillipe Girard, Clément Chion, Caroline Von Schilling, Rodolphe Coulon, and Patrick Verhaar. You guys made my workdays more pleasant with our coffee breaks. My dear friends Pedro, Taynara, Sophie, Leo, Aninha, Lucas, Natalia, Théo, you helped me a lot during the process of settling down. You guys were/are our family in Montreal. I have learnt a lot from you and I will never forget every moment shared with you (Does this call mean something?). Afshin, Mme Yanick and Mme Marie, «je vous remercie beaucoupe pour m'aider avec le frances!» I will never forget you. Mr. Richard Lancing, your blessing messages every sunday morning gave me peace and strength. Thank you very much.

Decomposição de séries temporais preservando o viés determinístico

“…Logo, as regras geradoras estimadas a partir desses espaços não se adéquam aos dados originais. De maneira complementar, ao modelar uma série predominantemente determinística, por meio de ferramental Estatístico, tende-se a subestimar as dependências existentes entre observações (RIOS, 2013). O cenário ideal se dá pela adoção de ambas abordagens sobre cada uma dessas influências presentes na série temporal original, ou seja, por meio do emprego do ramo Estatístico sobre as influências estocásticas e do ramo baseado em Sistemas Dinâmicos sobre as determinísticas.…”

“…Essa característica se deve à influência de fatores desconhecidos, os quais produzem influências aleatórias tipicamente provenientes da falta de precisão, erro de medição ou falta de conhecimento sobre o fenômeno observado. Assim, em cenários reais, séries temporais são tipicamente formadas por uma mistura desses dois componentes: o determinístico e o estocástico (RIOS, 2013).…”

“…O ramo Estatístico produz melhores resultados para séries temporais estocásticas, enquanto o baseado em Sistemas Dinâmicos é melhor para séries temporais determinísticas. Portanto, ambos se complementam e podem ser utilizados em conjunto, tal como proposto por Rios (2013). As seções seguintes apresentam maiores detalhes sobre esses dois ramos empregados na análise de séries temporais.…”

“…Conhecimentos prévios fazem com que pesquisadores adotem abordagens Estatísticas ou baseadas em Sistemas Dinâmicos para analisar séries temporais (RIOS, 2013). Essa opção única tende a causar problemas, pois tipicamente subestima influências estocásticas ou determinísticas presentes nos dados.…”

“…É possível observar que as primeiras IMFs apresentam altas frequências, as quais são tipicamente associadas ao comportamento estocástico. Nem sempre essa associação de estocasticidade com as altas frequências é verificada na prática, porém foi utilizada em diversos cenários estudados por Rios (2013).…”