Analysis of high-frequency financial data over different timescales: a Hilbert-Huang transform approach

This thesis provides a better understanding of the complex dynamics of high-frequency financial data. We develop a methodology that successfully and simultaneously character¬izes both the short and the long-term fluctuations latent in a time series. We extensively investigate the applications of the empirical mode decomposition (EMD) and the Hilbert transform to the analysis of intraday financial data. The applied methodology reveals the time-dependent amplitude and frequency attributes of non-stationary and non-linear time series. We uncover a scaling law that links the amplitude of the oscillating components to their respective period. We relate such scaling law to distinctive properties of financial markets. This research is relevant because financial data contain patterns specific to the observa¬tion frequency and are thus, of interest to different type of market agents (market traders, intraday traders, hedging strategist, portfolio managers and institutional investors), each characterized by a different reaction time to new information and by the frequency of its intervention in the market. Understanding how the investment horizons of these agents in¬teract may reveal significant details about the physical processes that generate or influence financial time series. We use the EMD to estimate volatility, generalising the idea of the popular realised volatility estimator by decomposing financial time series into several timescales compo¬nents which are related to different investment horizons. We also investigate the dynamic correlation at different timescales and at different time-lags, revealing a complex structure of financial signals. Following the multiscale analysis approach, we propose a novel empirical method to es¬timate a time-dependent scaling parameter in analogy to the scaling exponent for self-similar processes. Using numerical simulations, we investigate the robustness of our estimator to heavy-tailed distributions. We apply the scaling estimator to intraday stock market prices and uncover scaling properties which differ from what would be expected from a random walk. We also introduce a novel entropy-like measure which estimates the regularity of a time series. This measure of complexity can be used to identify periods of high and low volatility x which could help investors to choose the appropriate time for investment. Finally, we pro¬pose a multistep-ahead forecasting framework based on EMD combined with support vector regression. The originality of our models is the inclusion of a coarse-to-fine reconstruction step to analyse the forecasting capabilities of a combination of oscillating functions. We compare our models with popular benchmark models which do not use the EMD as a pre¬processing tool, obtaining better results with our proposed framework. Part of the research developed on this thesis is published in Physica A: Statistical Me¬chanics and its Applications [137] and in the European Physical Journal, Special Topics [136]. It was also presented at international conferences, including the 20th annual work¬shop on the Economic Science with Heterogeneous Interacting Agents (WEHIA) 2015 and the 21st Computing in Economics and Finance (CEF) conference 2015.