Comparação entre técnicas de redução de dimensionalidade em séries temporais: um foco na setorização de ativos em índices no mercado financeiro

Abstract

This study analyzed the application of the Uniform Manifold Approximation and Projection (UMAP) method in comparison to Principal Component Analysis (PCA) and t-distributed Stochastic Neighbor Embedding (t-SNE) in the clustering of assets in stock indexes, focusing on time series. The central problem addresses how the choice between linear methods, represented by PCA, and non-linear methods, such as t-SNE and UMAP, impacts the preservation of crucial information for the effective clustering of assets in indexes like Ibovespa and S&P 500. The research fills a gap in the literature by exploring the specificity of this choice, highlighting its technical and strategic importance in balancing efficiency and effectiveness. To conduct the experiments, different time horizons were analyzed by applying dimensionality reduction techniques to transform financial time series and subsequently clustering the resulting assets using algorithms such as K-Means, HDBSCAN, and GMM. The metrics used included the Silhouette Index, which evaluates the consistency of the clusters, and the Calinski-Harabasz Index, which measures their separation. The results emphasize Dimensionality Reduction as an essential tool to overcome the challenges posed by the Curse of Dimensionality in financial analyses. Methods such as UMAP proved particularly effective in revealing structural patterns in complex and multidimensional data, overcoming the limitations of linear techniques. This work not only reinforces the relevance of these techniques in practical applications but also provides a solid basis for future research and the development of solutions focused on analyzing high-dimensional financial data.