Francisco Javier Rodríguez Cortés

We propose a state‐space approach for a non‐parametric tv‐GARCH model. Using a number of non‐parametric techniques, we estimate slowly time‐varying curves for the parameters and combine it with a recursive system based on the Kalman filter as a methodological framework to obtain forecasts from the model. Our results based on Monte Carlo simulations and an application to the Selective Stock Price Index of the Chilean stock market indicate that the non‐parametric tv‐GARCH model shows the best fit and provides the best forecasting performance, compared with the stationary GARCH model and other techniques, such as tv‐GARCH with time‐varying parameters determined by deterministic functions. These results have relevant implications for risk management, portfolio diversification, and asset allocation.

This study introduces a novel method specifically designed to detect clusters of points within linear networks. This method extends a classification approach used for point processes in spatial contexts. Unlike traditional methods that operate on planar spaces, our approach adapts to the unique geometric challenges of linear networks, where classical properties of point processes are altered, and intuitive data visualisation becomes more complex. Our method utilises the distribution of the Kth nearest neighbour volumes, extending planar-based clustering techniques to identify regions of increased point density within a network. This approach is particularly effective for distinguishing overlapping Poisson processes within the same linear network. We demonstrate the practical utility of our method through applications to road traffic accident data from two Colombian cities, Bogota and Medellin. Our results reveal distinct clusters of high-density points in road segments where severe traffic accidents (resulting in injuries or fatalities) are most likely to occur, highlighting areas of increased risk. These clusters were primarily located on major arterial roads with high traffic volumes. In contrast, low-density points corresponded to areas with fewer accidents, likely due to lower traffic flow or other mitigating factors. Our findings provide valuable insights for urban planning and road safety management.

Coffee farming, a lifeline for numerous families in the mountainous regions of Latin America, faces challenges due to climate change and production variability, which complicate the use of forecast models at the territorial level. In response to these challenges, territorial inference has gained relevance, especially with the advancement of Geographic Information Systems (GIS), which provide useful tools for territorial analysis. Although spatial models are increasingly applied in GIS, coffee farming, like many agricultural subsectors, is hindered by a lack of information and spatial methodologies. This work proposes a methodology to identify spatial patterns of homogeneous production areas. Data from 140 farms, representing 3,900 members of the coffee grower cooperative of Andes, dispersed over 200,000 ha, were analyzed between 2019 and 2021. The variables used to measure productivity included the number of fruits per tree, the average fruit weight, planting density, and the conversion rate of cherry coffee to dry parchment coffee. A simple linear regression model was employed, and spatial dependency analyses were performed using the global and local Moran’s Index to identify clusters of territorial subdivisions. The data were processed in R language, and the GeoDa™ program was used to obtain the spatial weight matrix. Territorial units with similar characteristics for high quality mountain coffee production were identified through spatial dependency indicators. The methodology can contribute to estimating coffee production in large territories, improving the reliability of information and allowing for more informed decision-making to optimize coffee farming in mountainous areas.

The k-sample problem for functional data has been widely studied from theoretical and applied perspectives. In literature, Gaussianity of the generating process is generally assumed, which may be impractical in some situations. This work proposes an extension of the Kruskal-Wallis test to the case of functional data as an alternative to the problem of non- Gaussianity. The methodology used consisted of transforming each group's functional data into scalars using random projections and subsequently performing classical Kruskal-Wallis tests. The main results were the extension of the Kruskal-Wallis test to the case of functional data and the verification of its unbiased and consistency properties. Reducing dimensionality from random projections allows us to extend the classical Kruskal-Wallis test to the functional context and solve problems of non-Gaussianity and atypical observations.

El mar Caribe colombiano cuenta con reservas de hidrocarburos, diversidad ecosistémica, desarrollo de pesca, transporte marítimo, y el abastecimiento de redes de comunicación [1-3]. La región maneja una elevada demanda del espacio marino costero [2]. Por tanto, es necesario considerar un desarrollo sustentable y entender los riesgos físicos que implica, así como las dinámicas de los sistemas, y su afectación por las actividades antrópicas. El objetivo del trabajo es la identificación y análisis de elementos geológicos, climáticos y oceanográficos que se encuentran en zonas profundas y su incidencia sobres el territorio. El impacto de los elementos naturales, fue cuantificado mediante el índice ICI (Índice de Cuantificación de Impacto) propuesto en este trabajo y que resume diferentes fuentes de variación en un único valor. Se presenta un análisis estadístico de interacciones cualitativas para la comprensión de las problemáticas ambientales desde una visión biofísica y la generación de soluciones eficaces a las mismas.

We consider the problem of detection of features in the presence of clutter for spatio‐temporal point patterns. In previous studies, related to the spatial context, Kth nearest‐neighbor distances to classify points between clutter and features. In particular, a mixture of distributions whose parameters were estimated using an expectation‐maximization algorithm. This paper extends this methodology to the spatio‐temporal context by considering the properties of the spatio‐temporal Kth nearest‐neighbor distances. For this purpose, we make use of a couple of spatio‐temporal distances, which are based on the Euclidean and the maximum norms. We show close forms for the probability distributions of such Kth nearest‐neighbor distances and present an intensive simulation study together with an application to earthquakes.