Methodologies used to iinfer the dynamics of high dimensional time-series data.

该项目属于EPSRC统计与应用概率研究领域。我的研究重点是用于推断高维时间序列数据动态的方法。与Nikolaos Kantas和George Deligiannidis一起，我们的目标是对具有非马尔可夫潜在长记忆潜在状态的状态空间模型进行模型校准。目前最先进的方法包括粒子MCMC，其中关于过滤密度的信息存储在有限的粒子集合中。然而，这些方法存在维数、路径退化以及与数据集大小的可扩展性差等问题。为了克服这些问题，我正在研究扩散模型在时间序列中的应用，最初着眼于分数布朗运动的时间序列合成。我们未来的目标包括研究扩散模型如何很好地推断sde驱动时间序列的漂移和扩散系数，以及最终如何将它们应用于粒子滤波。另一方面，与Mihai Cucuringu和Guy Nason一起，我专注于高维时间序列的协方差结构建模，特别是金融时间序列和投资组合构建。以往关于协方差预测的文献多集中在M-GARCH模型上，而M-GARCH模型存在维数诅咒的问题。近年来，越来越多的文献将网络科学方法应用于建模和预测。在两位导师之前的研究基础上，我正在研究如何将自回归和网络效应纳入相关和协方差结构的模型中，灵活选择最大的自回归滞后和网络在每个滞后处的影响。从长远来看，我的目标是使用这些模型来构建更好的跨资产风险度量，并使用图聚类技术来构建提供更好回报的投资组合。

This project falls within the EPSRC Statistics and Applied Probability Research Area. My research focuses on methodologies used to infer the dynamics of high dimensional time-series data. Alongside Nikolaos Kantas and George Deligiannidis, we aim to perform model calibration on state space models with non-Markovian, potentially long-memory latent states. Current state-of-the-art approaches involve particle MCMC, where information on filtering density is stored in a finite set of particles. However, these methods suffer from the curse of dimensionality, path degeneracy, and scale poorly with the size of the dataset. To overcome these issues, I am investigating the application of diffusion models in time-series, initially with a look towards time-series synthesis of Fractional Brownian Motion. Our future aims include to investigate how well diffusion models can infer the drift and diffusion coefficients of SDE-driven time-series, and, ultimately, how they can be applied in particle filtering. On the other hand, alongside Mihai Cucuringu and Guy Nason, I am focusing on modelling the covariance structure of high dimensional time-series, with a specific focus on financial time-series and portfolio construction. Previous literature on covariance forecasting often focuses on M-GARCH models, which suffer from the curse of dimensionality. In recent years, a growing body of literature has applied network science methods for both modelling and forecasting. Building on previous research by both supervisors, I am investigating how to incorporate autoregressive and network effects in models for correlation and covariance structures, with flexibility in choosing the maximum autoregressive lag and the influence of the network at each lag. In the long-term, I aim to use these models to build better measures of cross-asset risk, and use graph clustering techniques to build portfolios that deliver better returns.