Novel methods for network-structured time series modelling

我们的研究重点是网络时间序列和长记忆时间序列。网络时间序列是一维分量通过图结构相互联系的多变量过程。这种类型的数据自然会出现在各种环境中，比如社交媒体，用户通过友谊或合作网络联系在一起。同样，来自其他领域的数据，如图像，可以转换为类似图形的结构，以便于分析。另一方面，长记忆(LM)过程是特定类型的时间序列，其特征是自相关性随着时间的缓慢衰减。由于文献中的现有网络模型并不是专门设计用于使用LM来处理数据，因此对能够利用该属性对网络时间序列进行建模的技术的需求日益增长。在我们的项目中，我们将长内存融入到网络环境中。了解长记忆网络时间序列的性质和行为对于发展合适的估计方法至关重要。具体地说，我们研究了各种参数估计方法，并提出了与长期相关数据相关的更广泛的网络时间序列领域中出现的一系列潜在问题。我们的方法将涉及数学技术，如参数估计方法、预测或用于探索性分析的统计工具。

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.