Multiscale analysis of financial volatility

• Main Author: Ghezelayagh, Bahar
• Published: University of East Anglia 2013
• Subjects: 332.01
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.687858

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.