Year

2016

Degree Name

Doctor of Philosophy

Department

School of Mathematics and Applied Statistics

Abstract

Countless processes, both natural and man made are driven by seemingly random processes. Measuring the randomness which dominates everything from the movements of stock market prices to the recordings on a seismograph is the first step towards understanding it. This thesis focused on measuring the volatility of financial time series, however the potential applications of the techniques developed herein are not limited to the financial realm.

The Hilbert-Huang Transform (HHT) is a powerful new tool which is well suited for the analysis of non-stationary and nonlinear time series. The literature exploring its potential applications to the analysis of financial data is surprisingly sparse considering its apparent suitability. This thesis developed and tested several techniques for estimating time series volatility, all of which use the HHT to break down financial data into simple wave like structures which facilitate analysis.

The estimation techniques developed were tested on low frequency data, namely ten years worth daily data for the NASDAQ and All Ords Indices. A simulated study to emulate high frequency data was also carried out to study volatility estimation in the presence of microstructure noise. Finally, several estimation techniques were used to give one step ahead predictions on the AUD/USD, GBP/USD and EUR/USD exchanges, a simulated options market was then set up in which differing predictions compete against one another.

The HHT based estimators were found to be competitive with the alternatives tested in the low frequency realm, with the added advantage that the technique is intuitive and can handle unevenly spaced data with ease. The HHT procedure was used as a low pass filter in order to sift off market microstructure and effectively measure volatility when the true price was obfuscated by market frictions. Finally, the construction of a simulated options market operating on real high frequency foreign exchange data showed that this filtering approach was also effective when real data was used.

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