Novel methods for network-structured time series modelling

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Our research focuses on network and long-memory time series. Network time series are multivariate processes in which one-dimensional components are interconnected through a graph structure. This type of data naturally occurs in various settings, such as social media, where users are connected through friendship or collaboration networks. Similarly, data from other domains, like images, can be transformed into graph-like structures for easier analysis. On the other hand, long memory (LM) processes are specific types of time series characterised by a slow decay of autocorrelation over time. This feature is quite common, and examples can be found in environmental records, computer traffic, and neuroscience data.Since existing network models in the literature are not specifically designed to handle data with LM, there is a growing demand for techniques capable of modelling network time series with this property. In our project, we incorporate long memory into the network setting. Understanding the properties and behaviour of long memory network time series is crucial for developing suitable estimation methods. Specifically, we investigate various parameter estimation methods and present a range of potential problems that arise in the broader field of network time series related to long-range dependent data.Our methodology will involve mathematical techniques, such as parameters estimation methods, forecasting or statistical tools for exploratory analysis.