Vives i Santa Eulàlia, Josep, 1963-Muñoz Martínez, Sergio Gabriel2023-10-252023-10-252023-06-12https://hdl.handle.net/2445/203142Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023 , Director: Josep Vives i Santa Eulàlia[en] Time series analysis plays a vital role in understanding various phenomena in a wide variety of fields. Over the years, more complex statistical models have been developed that allow us to analyze time series in a more accurate way. This project studies in depth one of them: the ARFIMA models. These models are very useful for examining long memory time series. The main purpose of this project is to provide a comprehensive analysis of these models, including their theoretical foundations, estimation methods and a practical implementation. In particular, the $R$ programming language is used to evaluate the possibility of modeling the time series that shows the air quality of Barcelona between 2017 and 2019 using an ARFIMA model.59 p.application/pdfcatcc-by-nc-nd (c) Sergio Muñoz Martı́nez, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/Processos estocàsticsAnàlisi de sèries temporalsModels lineals (Estadística)Estadística matemàticaTreballs de fi de grauStochastic processesTime-series analysisLinear models (Statistics)Mathematical statisticsBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess