A Network of two Markets, Correlations for Stocks in the S&P500 Index and Stocks Traded in the BMV

Una Red entre dos mercados, correlaciones entre acciones en el Índice S&P500 y acciones comercializadas en BMVNuestro objetivo es estudiar como las acciones de México y Estados Unidos están interconectadas. Aplicamos un método novedoso basado en un modelo gráfico. Estimamos correlaciones parciales para cada año del período 2000-2020. Nuestros resultados basados en matrices de correlaciones parciales muestran un nivel sistemático de interconectividad entre países que métricas de la teoría de redes confirman. Una diferencia importante entre estos países es como los sectores en cada mercado se enlazan. La mayoría de los sectores en los Estados Unidos están densamente interconectados. En contraste, sectores en México presentan menos enlaces. Después comparamos redes en los períodos de la crisis hipotecaria subprime y la crisis originada por la pandemia COVID-19. Las diferentes velocidades de propagación de ambas crisis son correctamente capturadas por las métricas. Una limitación surge de la información y es deseable incluir datos actualizados. El novedoso método utilizado, que llevó a obtener nuevos resultados, dota de originalidad al trabajo. Se concluye que datos desagregados son una dirección de investigación prometedora.Our goal is to study how stocks from Mexico and United States are interconnected. We apply a novel method based on a graphical model. We estimate partial correlations for every year of the period 2000-2020. Our results based on partial correlation matrices show a systematic level of inter-connectivity across countries that metrics from network theory confirm. An important difference between these countries is how sectors in each market are linked. Most sector graphs in the United States are densely interconnected. In contrast, sectors in Mexico present much less links. We then compare networks in the periods of the subprime mortgage crisis and the crisis triggered by the COVID-19 pandemic. The different propagation speeds of both crises are correctly captured by the metrics. A limitation is derived from information, and it is desirable to include actualized data in the study. The deployed novel method, which led to obtain new results, endow originality to the work. It is concluded that disaggregated data provides a promising venue of research

Explicit Solution of a Linearly Constrained Infinite Quadratic Problem

A norm minimization problem posed in K-dimensional finite arrays without non-negativity constraints was efficiently solved by Romero Romero. Going beyond we provide here an explicit, exact solution in case the arrays are replaced by L2-Hilbert spaces. Furthermore, we propose a polynomial procedure yielding an approximate optimal solution when non-negativity constraints must be taken into account for K = 2