Multiscale analysis of financial volatility

This thesis is concerned with the modeling of financial time series data. It introduces to the economics literature a set of techniques for this purpose that are rooted in engineering and physics, but almost unheard of in economics. The key feature of these techniques is that they combine the available information in the time and frequency domains simultaneously, making it possible to enjoy the advantages of both forms of analysis. The thesis is divided into three sections. First, after briefly outlining the Fourier methods, a more exible technique that allows for the study of time-scale dependent phenomena (motivated from a discussion on Heisenberg's uncertainty principle) namely Wavelet method is defined. A complete account of discrete and continuous wavelet transformations, and wavelet variation is provided and the advantages of wavelet-multiresolution analysis over Fourier methods are demonstrated. In the second section, the statistical properties of financial returns at 1-day, 5-day and 10-day sampling intervals are studied using S&P500 index for over a decade, and the links between dependence properties of financial returns at lower sampling frequencies are explored. The concepts of temporal aggregation and skip sampling are discussed and the effects of temporal aggregation on long range dependent time series are theoretically outlined and then tested through simulations and empirically via S&P500. In the third section, the variation of two years of five-minute GBP/USD exchange rate is analysed and the notion of realised variation is explored. The characteristics of the intraday data at different sampling frequencies (5-minute, 30-minute, 60-minute, 10-hour, 1-day, and 5-day) are compared with each other and filtered out from seasonalities using the wavelet multiscaling technique. We find that temporal aggregation does not change the decay rate of autocorrelation functions of long-memory data of certain frequencies, however the level at which the autocorrelation functions start from move upward for daily data. This thesis adds to the literature by outlining and comparing the effects of aggregation between daily and intra-daily frequencies for the realised variances, which to our knowledge is a first. The effect temporal aggregation has on daily data is different from intra-daily data, and we provide three reasons why this might be. First, at higher frequencies strong periodocities distort the autocorrelation functions which could bring down the decay rate and mask the long memory feature of the data. Second, the choice of realised variance is crucial in this matter and different functions can result in contradictory outcomes. Third, as the order of aggregation increases the decay rate does not depend on the order of the aggregation

Long memory in volatility, modelling and forecasting in the wavelet domain

Imperial Users onl

Intraday dynamics of stock market returns and volatility

This paper provides new empirical evidence for intraday scaling behavior of stock market returns utilizing a 5 min stock market index (the Dow Jones Industrial Average) from the New York Stock Exchange. It is shown that the return series has a multifractal nature during the day. In addition, we show that after a financial “earthquake”, aftershocks in the market follow a power law, analogous to Omori's law. Our findings indicate that the moments of the return distribution scale nonlinearly across time scales and accordingly, volatility scaling is nonlinear under such a data generating mechanism

Are the scaling properties of bull and bear markets identical? Evidence from oil and gold markets

In this study, the scaling properties of the oil and gold return volatilities have been analyzed in the context of bull and bear periods. In the determination of bull and bear turning points, we used the Modified Bry-Boschan Quarterly (MBBQ) algorithm. Results showed that the business cycle phase shapes of the bear periods in the oil market are almost linear, whereas the bull and bear periods of the gold and bull period of the oil market are convex. This means that there are sharper declines in the bear period of the oil market. Following the detection of bull and bear periods, scaling exponent H analysis was performed via the aggregated variance, Higuchi’s statistic, Peng’s statistic, rescaled range, boxed periodogram and wavelet fit models, which are from the time, frequency and wavelet domains. As there are conflicts about the credibility of these methods in the literature, we have used the shuffling procedure in order to determine the most robust methods. According to the results, bear periods have higher volatility persistency than bull periods. © 2014 by the author; licensee MDPI, Basel, Switzerland

An analysis of spending behaviour under liquidity constraints with an application to financial hedging

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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

Intraday dynamics of stock market returns and volatility

This paper provides new empirical evidence for intraday scaling behavior of stock market returns utilizing a 5 min stock market index (the Dow Jones Industrial Average) from the New York Stock Exchange. It is shown that the return series has a multifractal nature during the day. In addition, we show that after a financial "earthquake", aftershocks in the market follow a power law, analogous to Omori's law. Our findings indicate that the moments of the return distribution scale nonlinearly across time scales and accordingly, volatility scaling is nonlinear under such a data generating mechanism. © 2006 Elsevier B.V. All rights reserved

Dependence structure in financial time series: Applications and evidence from wavelet analysis

Conventional time series theory and spectral analysis have independently achieved significant popularity in mainstream economics and finance research over long periods. However, the fact remains that each is somewhat lacking if the other is absent. To overcome this problem, a new methodology, wavelet analysis, has been developed to capture all the information localized in time and in frequency, which provides us with an ideal tool to study non-stationary time series. This paper aims to explore the application of a variety of wavelet-based methodologies in conjunction with conventional techniques, such as the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models and long-memory parameter estimates, in analysing the short and long term dependence structure of financial returns and volatility. Specifically, by studying the long-memory property of these time series we hope to identify the source of their possible predictability. Above all else, we document the indispensable role of trading activities associated with low frequencies in determining the long-run dependence of volatility. It follows that GARCH models incorporating long-memory and asymmetric returns-volatility dynamics can provide reasonably accurate volatility forecasts. Additionally, the persistence parameter of returns, represented by the Hurst index, is observed to be correlated to trading profits obtained from typical technical rules designed to detect and capitalize on existing trending behaviour of stock prices. This implies that the Hurst index can be used as a good indicator of the long-memory characteristic of the market, which in turn drives such trending behaviour