Maria Eduarda Silva

Abstract
Time series data are essential for a wide range of applications, yet access to high-quality datasets is often constrained by privacy concerns, acquisition costs, and labeling challenges. Synthetic time series generation has emerged as a promising approach to address these limitations. In this work, we investigate the use of complex network mappings for synthetic time series generation, focusing on the Quantile Graph (QG) representation and its inverse. While the inverse QG mapping has been previously proposed, its potential as a general-purpose data generator has not been systematically evaluated. We address this gap through a comprehensive empirical study assessing both the fidelity and utility of synthetic time series generated by the Inverse Quantile Graph (InvQG) framework. The evaluation combines statistical feature analysis, network-based topological characteristics, and performance in downstream clustering and classification tasks, using simulated and real-world datasets. The results show that InvQG effectively preserves marginal distributions and short-term temporal dependencies across a wide range of models, while exhibiting predictable limitations in capturing long-range or higher-order dynamics.

Abstract
Analyzing time series of counts often encounters the challenge of missing data, which can significantly hinder the accuracy and reliability of statistical models. This study addresses this issue by employing Poisson first-order integer-valued au-toregressive (PoINAR) models in conjunction with the Gibbs sampler with data augmentation. This method is particularly effective as it accounts for both the mechanisms behind missing data and the intrinsic serial correlation within the time series. Two distinct approaches to data augmentation are explored and compared in this work and illustrated using both simulated and real data.

Abstract
Atlantic salmon populations have declined in many regions and are affected by several natural and anthropogenic factors throughout their lives. We investigated the role of environmental drivers and the effect of dam construction on the trend in catches of spawning adults of a migratory population currently at risk. For this purpose, we examined the salmon catches from 1914 to 2020 in the Minho River (NW Portugal, SW Europe), located at the southern limit of this species' distribution. There was a decline in catches over time with an inverse and significant relationship between the trend in catches and lagged temperature. Delayed effects of this type may indicate temperature influences on survival during early life history stages. Similarly, the trend in catches decreased with the increasing number of dams. A forecast model built for the period before the construction of the first major dam in this river (before 1955), including lagged temperature, resulted in a decreasing trend in the number of catches. This demonstrates that catches would have declined due to temperature effects even without dam construction. This does not diminish the role of dams in the observed decline; rather, it reveals that temperature-driven declines would have occurred independently. Nonetheless, efficient management and conservation of this imperiled population require further detailed biological information on the number of returning spawning adults and salmons' survival throughout their life cycle.

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.