Conference Agenda

A novel time series framework is proposed which addresses all relevant empirical properties of a time series, making it an essentially universal model. More specifically, the dynamics in all conditional moments of a suitable continuous or discrete distribution are modeled jointly and without the need to make restrictive assumptions about the functional form of the link functions. Furthermore, all considered explanatory variables are allowed to exhibit nonlinear and potentially time-varying effects on the conditional moments. This can be achieved by employing a simple feedforward neural network with a single hidden layer and an output for each conditional moment (parameter). In contrast to many (deep) neural network approaches, the proposed model is stochastically interpretable and allows for the calculation of standard errors, and in particular, confidence intervals. Many conventional time series frameworks such as (integer-valued) GARCH can be interpreted as simplified special cases of the proposed model. Several empirical applications are presented to illustrate the capabilities and the implementation.

Research on count time series has grown substantially, leading to the development of numerous models designed to capture key characteristics such as trends, seasonality, overdispersion, outliers, and complex dependence structures. Despite these advances, the evaluation of such models remains challenging due to the limited availability of real-world count time series. This scarcity often forces researchers to illustrate new methods using only a few datasets, which restricts systematic comparison and hinders robust performance assessment. Addressing this gap is essential for advancing methodological development and ensuring practical applicability in diverse domains.
In this presentation, we focus on the generation of synthetic count time series that can exhibit a wide range of controlled behaviors. Our approach relies on Mixture INAR (MixINAR) models and a set of descriptive features designed to summarize key properties of count data. We first discuss which features are most suitable for characterizing count time series and then show how they can be used to guide the simulation of diverse collections of synthetic data. By comparing the simulated series with commonly used benchmark datasets, we illustrate how realistic and flexible the generated time series can be. Overall, this work provides a practical way to create representative collections of count time series, supporting more thorough testing and comparison of models in this area.

This work is financed by National Funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P. (Portuguese Foundation for Science and Technology) within the project TSP2Net, with reference 2023.13039.PEX, https://doi.org/10.54499/2023.13039.PEX

INAR and INGARCH-type processes are widely used approaches to model time series of counts. In this talk, I will speak about a class of generalized INARMA (integer-valued autoregressive) models which contains both of the aforementioned types of models as special cases. Notably I will outline a generalization of the INAR model which parallels the extension of the INARCH to the INGARCH process. Special attention is given to inference questions. These include maximum likelihood, moment-based and Gaussian quasi-likelihood techniques for parameter estimation. Moreover, I will discuss various testing problems. The developed methods are illustrated in simulation studies and a data example on childhood diseases in the German state of Bavaria.