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
Greenland ice core records display abrupt transitions, designated as Dansgaard-Oeschger (DO) events, characterised by episodes of rapid warming (typically decades) followed by a slower cooling. The identification of abrupt transitions is hindered by the typical low resolution and small size of paleoclimate records, and their significant temporal variability. Furthermore, the amplitude and duration of the DO events varies substantially along the last glacial period, which further hinders the objective identification of abrupt transitions from ice core records Automatic, purely data-driven methods, have the potential to foster the identification of abrupt transitions in palaeoclimate time series in an objective way, complementing the traditional identification of transitions by visual inspection of the time series.In this study we apply an algorithmic time series method, the Matrix Profile approach, to the analysis of the NGRIP Greenland ice core record, focusing on:- the ability of the method to retrieve in an automatic way abrupt transitions, by comparing the anomalies identified by the matrix profile method with the expert-based identification of DO events;- the characterisation of DO events, by classifying DO events in terms of shape and identifying events with similar warming/cooling temporal patternThe results for the NGRIP time series show that the matrix profile approach struggles to retrieve all the abrupt transitions that are identified by experts as DO events, the main limitation arising from the diversity in length of DO events and the method’s dependence on fixed-size sub-sequences within the time series. However, the matrix profile method is able to characterise the similarity of shape patterns between DO events in an objective and consistent way.

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.