[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.

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023 , Director: Josep Vives i Santa Eulàlia