Maria Eduarda Silva

Abstract
Multivariate time series analysis is a vital but challenging task, with multidisciplinary applicability, tackling the characterization of multiple interconnected variables over time and their dependencies. Traditional methodologies often adapt univariate approaches or rely on assumptions specific to certain domains or problems, presenting limitations. A recent promising alternative is to map multivariate time series into high-level network structures such as multiplex networks, with past work relying on connecting successive time series components with interconnections between contemporary timestamps. In this work, we first define a novel cross-horizontal visibility mapping between lagged timestamps of different time series and then introduce the concept of multilayer horizontal visibility graphs. This allows describing cross-dimension dependencies via inter-layer edges, leveraging the entire structure of multilayer networks. To this end, a novel parameter-free topological measure is proposed and common measures are extended for the multilayer setting. Our approach is general and applicable to any kind of multivariate time series data. We provide an extensive experimental evaluation with both synthetic and real-world datasets. We first explore the proposed methodology and the data properties highlighted by each measure, showing that inter-layer edges based on cross-horizontal visibility preserve more information than previous mappings, while also complementing the information captured by commonly used intra-layer edges. We then illustrate the applicability and validity of our approach in multivariate time series mining tasks, showcasing its potential for enhanced data analysis and insights.

Abstract
The presence of missing data poses a common challenge for time series analysis in general since the most usual requirement is that the data is equally spaced in time and therefore imputation methods are required. For time series of counts, the usual imputation methods which usually produce real valued observations, are not adequate. This work employs Bayesian principles for handling missing data within time series of counts, based on first-order integer-valued autoregressive (INAR) models, namely Approximate Bayesian Computation (ABC) and Gibbs sampler with Data Augmentation (GDA) algorithms. The methodologies are illustrated with synthetic and real data and the results indicate that the estimates are consistent and present less bias when the percentage of missing observations decreases, as expected. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

Abstract
In recent years, there has been a surge in the prevalence of high- and multidimensional temporal data across various scientific disciplines. These datasets are characterized by their vast size and challenging potential for analysis. Such data typically exhibit serial and cross-dependency and possess high dimensionality, thereby introducing additional complexities to conventional time series analysis methods. To address these challenges, a recent and complementary approach has emerged, known as network-based analysis methods for multivariate time series. In univariate settings, quantile graphs have been employed to capture temporal transition properties and reduce data dimensionality by mapping observations to a smaller set of sample quantiles. To confront the increasingly prominent issue of high dimensionality, we propose an extension of quantile graphs into a multivariate variant, which we term Multilayer Quantile Graphs. In this innovative mapping, each time series is transformed into a quantile graph, and inter-layer connections are established to link contemporaneous quantiles of pairwise series. This enables the analysis of dynamic transitions across multiple dimensions. In this study, we demonstrate the effectiveness of this new mapping using synthetic and benchmark multivariate time series datasets. We delve into the resulting network's topological structures, extract network features, and employ these features for original dataset analysis. Furthermore, we compare our results with a recent method from the literature. The resulting multilayer network offers a significant reduction in the dimensionality of the original data while capturing serial and cross-dimensional transitions. This approach facilitates the characterization and analysis of large multivariate time series datasets through network analysis techniques.

Abstract
Predictors of macroeconomic indicators rely primarily on traditional data sourced from National Statistical Offices. However, new data sources made available from recent technological advancements, namely data from online activities, have the potential to bring about fresh perspectives on monitoring economic activities and enhance the accuracy of forecasting. This paper reviews the literature on predicting macroeconomic indicators, such as the gross domestic product, unemployment rate, consumer price index or private consumption, based on online activity data sourced from Google Trends, Twitter (rebranded to X) and mobile devices. Based on a systematic search of publications indexed on the Web of Science and Scopus databases, the analysis of a final set of 56 publications covers the publication history of the data sources, the methods used to model the data and the predictive accuracy of information from such data sources. The paper also discusses the limitations and challenges of using online activity data for macroeconomic predictions. The review concludes that online activity data can be a valuable source of information for predicting macroeconomic indicators. However, one must consider certain limitations and challenges to improve the models' accuracy and reliability. © 2024 - IOS Press. All rights reserved.

Abstract
Policymakers often have to make decisions based on incomplete economic data because of the usual delay in publishing official statistics. To circumvent this issue, researchers use data from Google Trends (GT) as an early indicator of economic performance. Such data have emerged in the literature as alternative and complementary predictors of macroeconomic outcomes, such as the unemployment rate, featuring readiness, public availability and no costs. This study deals with extensive daily GT data to develop a framework to nowcast monthly unemployment rates tailored to work with real-time data availability, resorting to Mixed Data Sampling (MIDAS) regressions. Portugal is chosen as a use case for the methodology since extracting GT data requires the selection of culturally dependent keywords. The nowcasting period spans 2019 to 2021, encompassing the time frame in which the coronavirus pandemic initiated. The findings indicate that using daily GT data with MIDAS provides timely and accurate insights into the unemployment rate, especially during the COVID-19 pandemic, showing accuracy gains even when compared to nowcasts obtained from typical monthly GT data via traditional ARMAX models.