The HJ biplot is a multivariate analysis technique that allows us to represent both individuals and variables in a space of reduced dimensions. To adapt this approach to massive datasets, it is necessary to implement new techniques that are capable of reducing the dimensionality of the data and improving interpretation. Because of this, we propose a modern approach to obtaining the HJ biplot called the elastic net HJ biplot, which applies the elastic net penalty to improve the interpretation of the results. It is a novel algorithm in the sense that it is the first attempt within the biplot family in which regularisation methods are used to obtain modified loadings to optimise the results. As a complement to the proposed method, and to give practical support to it, a package has been developed in the R language called SparseBiplots. This package fills a gap that exists in the context of the HJ biplot through penalized techniques since in addition to the elastic net, it also includes the ridge and lasso to obtain the HJ biplot. To complete the study, a practical comparison is made with the standard HJ biplot and the disjoint biplot, and some results common to these methods are analysed.

This paper aims to categorize countries by their e-participation index, according to political, capacity, and governmental environment factors; examine how they are projected based on these factors; and analyze whether this projection corresponds to the current state of e-participation development. It is the first study to provide an overview of the e-participation level using multivariate analysis techniques for three-way data analysis, specifically, the X-STATIS methodology and cluster analysis. These techniques enable the simultaneous representation of countries, factors, conditions, trajectories, and groupings, taking into account national conditions in the evolution of e-participation from 2008 to 2016. The results show that when the conditions of each country interact with the level of e-participation development, and depending on the economic development, 7% of countries are lagging behind in e-participation evolution, given their institutional and political capacity. This delay is particularly relevant in countries that enjoy a higher level of socioeconomic status. Meanwhile, 38% are above the level they would correspond to.

The Panama Canal, inaugurated in 1914, continues to play a pivotal role in global maritime connectivity. In 2016, the Canal underwent a significant expansion, reshaping maritime transit by accommodating larger vessels and reinforcing its strategic importance in international trade. The objective of this study is to identify a suitable time series statistical model to forecast the number of vessels transiting the Panama Canal. The three approaches employed were the following: the Autoregressive Integrated Moving Average (ARIMA) model, the Holt–Winters (HW) exponential smoothing method, and the Neural Network Autoregressive (NNAR) model. The models were compared based on forecasting errors to evaluate their predictive accuracy. Overall, the NNAR model exhibited slightly better predictive performance than the SARIMA (1,0,1) (0,1,1) model in terms of error, with both outperforming the Holt–Winters model by a significant margin.