Time-scale and memory in financial time series: a data mining approach
File(s)
Author(s)
Tzouras, Spilios
Type
Thesis
Abstract
Financial time series analysis is a highly empirical discipline concerned with the evolution
of the price of an asset. The key feature that distinguishes financial time series
from time series of other scientific domains is the element of uncertainty that they contain.
The recent financial crisis has tested the capabilities of several existing models
and evidenced the need for methods able to deal with the high complexity and the
non-stationary characteristics of the data observed in financial markets. The objective
of this thesis is to provide a better understanding of financial time series, to enhance the
abilities of existing methods, especially their predictive performance but also to develop
novel methods which aim to provide inferences in the presence of non-stationarities and
reduce the complexity of high dimensional tasks. To this end, the memory in the magnitude
and the memory in the sign of logarithmic returns is studied and a novel model
is constructed whose fit suggests that long memory might be present in the volatility
process and that when memory in the sign increases so does the memory in the magnitude.
Additionally, wavelets are employed for that they operate in both the time and
frequency domains. Thus, classic time series models and other methods extensively used
in the time domain are deployed across different frequency bands to combine knowledge
from both domains and provide information that might not be accessible otherwise. In
particular, the volatility process is modeled in the time domain after some of the noisy
behavior that exists in high frequencies, which might also contain outliers, is neglected.
Moreover, the volatility process is modeled directly in the wavelet domain in a scale-by-
scale manner in an effort to improve the forecasting performance. Furthermore, we
attempt to detect changes in the autocorrelation function of a process, which result
in changes in the spectral density function, by monitoring the wavelet variance across
different multiresolution scales.
of the price of an asset. The key feature that distinguishes financial time series
from time series of other scientific domains is the element of uncertainty that they contain.
The recent financial crisis has tested the capabilities of several existing models
and evidenced the need for methods able to deal with the high complexity and the
non-stationary characteristics of the data observed in financial markets. The objective
of this thesis is to provide a better understanding of financial time series, to enhance the
abilities of existing methods, especially their predictive performance but also to develop
novel methods which aim to provide inferences in the presence of non-stationarities and
reduce the complexity of high dimensional tasks. To this end, the memory in the magnitude
and the memory in the sign of logarithmic returns is studied and a novel model
is constructed whose fit suggests that long memory might be present in the volatility
process and that when memory in the sign increases so does the memory in the magnitude.
Additionally, wavelets are employed for that they operate in both the time and
frequency domains. Thus, classic time series models and other methods extensively used
in the time domain are deployed across different frequency bands to combine knowledge
from both domains and provide information that might not be accessible otherwise. In
particular, the volatility process is modeled in the time domain after some of the noisy
behavior that exists in high frequencies, which might also contain outliers, is neglected.
Moreover, the volatility process is modeled directly in the wavelet domain in a scale-by-
scale manner in an effort to improve the forecasting performance. Furthermore, we
attempt to detect changes in the autocorrelation function of a process, which result
in changes in the spectral density function, by monitoring the wavelet variance across
different multiresolution scales.
Version
Open Access
Date Issued
2015-03
Date Awarded
2015-09
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
McCoy, Emma J
Anagnostopoulos, Christoforos
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)