Novel methods for network-structured time series modelling

我们的研究重点是网络和长记忆时间序列。网络时间序列是多维过程，其中一维分量通过图结构相互连接。这种类型的数据自然会出现在各种环境中，比如社交媒体，用户通过友谊或协作网络联系在一起。同样，来自其他领域（如图像）的数据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，其特征是自相关随时间缓慢衰减。这个特征非常普遍，可以在环境记录、计算机流量和神经科学数据中找到例子。由于文献中现有的网络模型并不是专门为LM处理数据而设计的，因此对具有这种特性的网络时间序列建模技术的需求日益增长。在我们的项目中，我们将长内存集成到网络设置中。了解长记忆网络时间序列的性质和行为对于开发合适的估计方法至关重要。具体来说，我们研究了各种参数估计方法，并提出了一系列潜在的问题，这些问题出现在与远程依赖数据相关的更广泛的网络时间序列领域。我们的方法论将涉及数学技术，如参数估计方法，预测或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.