Contagion Patterns Classification in Stock Indices: A Functional Clustering Analysis Using Decision Trees

This paper aims to identify the main determinants of the countries that present contagion during the period 2000–2021, based on the determination of the behavior patterns of 18 stock market indices of 15 of the main economies. To do that, first, the B-spline method and Bezier curves are used to smooth observations by minimizing the noise. Subsequently, the Functional Principal Component Analysis (FPCA) methodology is applied. Then, the K-means clustering algorithm is used to determine the main groups using the silhouette method and cross-validation, considering the sum of squares of the distances as the function to minimize. Finally, classification trees and macroeconomic and financial analyses are used to determine the rules of variables that give a direct explanation of the contagion (clustering) between the stock indices. The main empirical results obtained suggest that the most significant macroeconomic variables are the Gross Domestic Product, the Consumer Price Index, and Foreign Direct Investment, while in the financial aspect and the most representative are Domestic Credit and number of companies listed on the stock market. It is worth noticing that government spending does not have a significant effect at any time as a determinant of contagion. Finally, it is important to mention, and surprising, that Mexico’s IPC was not clustered in the same group of US stock market indices anytime, despite the strong commercial relationship and the geographical closeness.