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
