Functional data analysis: methods and a study case in Ecuador - Portilla Morales, Jonathan Israel (2022)
Nowadays, we have seen the growth of all kinds of data, as well as the rise of data sciences. An example of this is Functional Data Analysis (FDA), which gives us a wide range of functions to study, analyze and project the reality of this data. Recently, there has been a great interest in applying FDA in different areas of study in Ecuador. One of these areas is meteorology. The present work has two parts; first, we will use FDA to analyze the annual temperature and precipitation rate through data provided by three meteorological stations in Ecuador: Quito, Inguincho, and San Gabriel between the years 1988 and 2018. In the second part, we will analyze the results of Principal Component Analysis (PCA) applied to functional data or better known as Functional Principal Component Analysis (FPCA), in three different cases with one replication, two replications, and three replications. Because FPCA works with covariance (correlation) matrices, we have observed that the first case is obsolete in the face of this method. For the cases with two to three replications, we have obtained three different ways of explaining the results. Finally, we have seen that it is advisable to apply more variables for future work to appreciate the overall effectiveness of Functional Principal Component Analysis.