A nonstationary seasonal Dynamic Factor Model: an application to temperature time series from the state of Minas Gerais

In many scientific fields, such as agriculture, temperature time series are of interest both as explanatory variables and as objects of study in their own right. However, at the state level, incorporating information from all possible locations in an analysis can be overwhelming, while using a summary measure, such as the state-wide average temperature, can result in significant information loss. In this context, using Dynamic Factor Models (DFMs) provides a compelling alternative for analyzing such multivariate time series, as they allow for the extraction of a small number of common factors that capture the majority of the variability in the data. Given that temperature series are typically seasonal, this study applies a nonstationary seasonal DFM to analyze a multivariate temperature time series from the state of Minas Gerais. The results show that the data can be effectively represented by two seasonal factors: the first captures the general seasonal pattern of the state, while the second contrasts the months of highest annual temperatures between two distinct regions.