Maria Eduarda Silva

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
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
Palaeoclimate time series, reflecting the state of Earth's climate in the distant past, occasionally display very large and rapid shifts showing abrupt climate variability. The identification and characterisation of these abrupt transitions in palaeoclimate records is of particular interest as this allows for understanding of millennial climate variability and the identification of potential tipping points in the context of current climate change. Methods that are able to characterise these events in an objective and automatic way, in a single time series, or across two proxy records are therefore of particular interest. In our study the matrix profile approach is used to describe Dansgaard-Oeschger (DO) events, abrupt warmings detected in the Greenland ice core, and Northern Hemisphere marine and continental records. The results indicate that canonical events DO-19 and DO-20, occurring at around 72 and 76 ka, are the most similar events over the past 110 000 years. These transitions are characterised by matching transitions corresponding to events DO-1, DO-8, and DO-12. They are abrupt, resulting in a rapid shift to warmer conditions, followed by a gradual return to cold conditions. The joint analysis of the delta 18O and Ca2+ time series indicates that the transition corresponding to the DO-19 event is the most similar event across the two time series.

Abstract
Seasonal and daily variations of gaseous emissions from naturally ventilated dairy cattle barns are important figures for the establishment of effective and specific mitigation plans. The present study aimed to measure methane (CH4) and ammonia (NH3) emissions in three naturally ventilated dairy cattle barns covering the four seasons for two consecutive years. In each barn, air samples from five indoor locations were drawn by a multipoint sampler to a photoacoustic infrared multigas monitor, along with temperature and relative humidity. Milk production data were also recorded. Results showed seasonal differences for CH4 and NH3 emissions in the three barns with no clear trends within years. Globally, diel CH4 emissions increased in the daytime with high intra-hour variability. The average hourly CH4 emissions (g h-1 livestock unit- 1 (LU)) varied from 8.1 to 11.2 and 6.2 to 20.3 in the dairy barn 1, from 10.1 to 31.4 and 10.9 to 22.8 in the dairy barn 2, and from 1.5 to 8.2 and 13.1 to 22.1 in the dairy barn 3, respectively, in years 1 and 2. Diel NH3 emissions highly varied within hours and increased in the daytime. The average hourly NH3 emissions (g h-1 LU-1) varied from 0.78 to 1.56 and 0.50 to 1.38 in the dairy barn 1, from 1.04 to 3.40 and 0.93 to 1.98 in the dairy barn 2, and from 0.66 to 1.32 and 1.67 to 1.73 in the dairy barn 3, respectively, in years 1 and 2. Moreover, the emission factors of CH4 and NH3 were 309.5 and 30.6 (g day- 1 LU-1), respectively, for naturally ventilated dairy cattle barns. Overall, this study provided a detailed characterization of seasonal and daily gaseous emissions variations highlighting the need for future longitudinal emission studies and identifying an opportunity to better adequate the existing mitigation strategies according to season and daytime.