Abstract
This study aims at characterizing the spatial and temporal dynamics of spatio-temporal data sets, characterized by high resolution in the temporal dimension which are becoming the norm rather than the exception in many application areas, namely environmental modelling. In particular, air pollution data, such as NO2 concentration levels, often incorporate also multiple recurring patterns in time imposed by social habits, anthropogenic activities and meteorological conditions. A two-stage modelling approach is proposed which combined with a block bootstrap procedure correctly assesses uncertainty in parameters estimates and produces reliable confidence regions for the space-time phenomenon under study. The methodology provides a model that is satisfactory in terms of goodness of fit, interpretability, parsimony, prediction and forecasting capability and computational costs. The proposed framework is potentially useful for scenario drawing in many areas, including assessment of environmental impact and environmental policies, and in a myriad applications to other research fields.

Abstract
Outlying observations are commonly encountered in the analysis of time series. In this paper a Bayesian approach is employed to detect additive outliers in order one Poisson integer-valued autoregressive time series. The methodology is informative and allows the identification of the observations which require further inspection. The procedure is illustrated with simulated and observed data sets.

Abstract
We introduce a new class of integer-valued self-exciting threshold models, which is based on the binomial autoregressive model of order one as introduced by McKenzie (Water Resour Bull 21:645-650, 1985. doi:. Basic probabilistic and statistical properties of this class of models are discussed. Moreover, parameter estimation and forecasting are addressed. Finally, the performance of these models is illustrated through a simulation study and an empirical application to a set of measle cases in Germany.

Abstract
This paper introduces new classes of bivariate time series models being useful to fit count data time series with a finite range of counts.. Motivation comes mainly from the comparison of schemes for monitoring tourism demand, stock data, production and environmental processes. All models are based on the bivariate binomial distribution of Type II. First, a new family of bivariate integer-valued GARCH models is proposed. Then, a new bivariate thinning operation is introduced and explained in detail. The new thinning operation has a number of advantages including the fact that marginally it behaves as the usual binomial thinning operation and also that allows for both positive and negative cross-correlations. Based upon this new thinning operation, a bivariate extension of the binomial autoregressive model of order one is introduced. Basic probabilistic and statistical properties of the model are discussed. Parameter estimation and forecasting are also covered. The performance of these models is illustrated through an empirical application to a set of rainy days time series collected from 2000 up to 2010 in the German cities of Bremen and Cuxhaven.

Abstract

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.