APPLICATIONS OF GRAPH THEORY AND MACHINE LEARNING IN TIME SERIES ANALYSIS AND SIGNAL PROCESSING: FROM FINANCIAL TIME SERIES TO MUSIC AUDIO

Abstract

In modern literature, academics are dichotomous whether stock price movements are random or not. In this thesis, we take advantage of the Horizontal Visibility Graph, a technique for mapping a time series into a graph representation, to shed light on the underlying dynamics of financial markets. A long-term analysis of the S&P 500 index using high-frequency data provides evidence that the index behaves as a chaotic process. This implies the presence of an underlying non-linear and deterministic structure. A short-term analysis reveals the time-varying dynamics where specific events, such as financial crises, have an impact on the behaviour of the index. Chaotic systems operate at and transition between different phases. A question that raises naturally is how one can pinpoint when the transition occurs, a task known as change point detection, and how we can identify distinct periods where the system operates at the same phase, a task known as semantic segmentation. The first task is well studied in literature, yet, only limited work is available on the latter one. We introduce a graph-based unsupervised learning algorithm performing both tasks while considering the multi-resolution nature of financial series. Fixed-size segments of the index series are represented as nodes in the graph and, intuitively, nodes belonging to the same community represent a semantic class. Due to lack of annotated time series in the domain of finance, we initially develop and test the performance of the algorithm using annotated music audio signals. Then, we calibrate the proposed approach to process real life signals where the presence of noise requires for special treatment. An application in the financial domain is illustrated using daily data for the S&P 500 index. In the last part of the thesis, we detour from the uni-variate time series analysis towards a multi-variate analysis. We present a price anomaly in the US security markets allowing investors to benefit from superior returns. By modelling inter-dependencies between stocks in the market as a graph, where nodes represent various equities, we introduce the interconnectedness factor. Results indicate that peripheral assets in the financial graph consistently outperform the central ones and the excess return is related to the exposure to systematic risk. The findings improve the understanding of systematic risk and advance current asset pricing models. Even though financial time series are not predictable long term, market inefficiencies enable investors to identify opportunities leading to sustainable long-term returns.

Date of Award	31 Dec 2022
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Xiaojun Zeng (Supervisor) & George Wang (Supervisor)