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

2025-10-17

AI Summary

In regional temperature analysis, statewide averaging obscures spatial heterogeneity, while high-dimensional station-level data induce redundancy and computational overload. To address this dual challenge, we propose a Non-Stationary Seasonal Dynamic Factor Model (NS-DFM), which incorporates time-varying factor loadings and seasonally varying periodic components to jointly extract two dominant factors: one capturing the state-level aggregate seasonal trend and the other characterizing regional disparities in peak-temperature months. Empirical evaluation on multi-source temperature time series from Minas Gerais, Brazil, demonstrates that just two factors account for over 90% of spatiotemporal variability—substantially outperforming conventional stationary DFM and static aggregation approaches. This work is the first to endogenize both non-stationarity and seasonal dynamics within a dynamic factor framework, enabling interpretable dimensionality reduction of high-dimensional climate data while explicitly quantifying spatial heterogeneity.

Technology Category

Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal DataKnowledge Representation and Reasoning: Geometric, Spatial, and Temporal ReasoningMachine Learning: Dimensionality Reduction/Feature Selection

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalizationSecurity and Privacy: Large-scale security measurements

Abstract

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.

Problem

• Modeling seasonal temperature patterns with dynamic factors
• Extracting common factors from multivariate temperature data
• Reducing information loss in state-level climate analysis

Innovation

• Nonstationary seasonal Dynamic Factor Model application
• Extracting two seasonal factors from temperature data
• Capturing regional temperature contrasts and seasonal patterns