Green, Elena (2014) Analysis and Modelling of Financial Logarithmic Return Data using Multifractal and Agent-Based Techniques. PhD thesis, National University of Ireland Maynooth.
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Elena Green.Analysis and modelling of Financial Logarithmic Return Data using Multifractal and Agent-Based Techniques.pdf
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Abstract
In recent years physicists have become involved in studying the financial market and
the vast data it generates. The constantly-updated streams of information are a perfect
testing ground for the hypothesis that the laws of statistical physics might apply to human
behaviour.
In this thesis, I study two empirical log return time series for the stylised facts of
financial data. I then use Multifractal Detrended Fluctuation Analysis to study the
empirical log returns for multifractal scaling. I find that extreme events are inimical to
the scaling in highly leptokurtic data. I also find that the temporal correlations in the
data are crucial to the scaling whereas the shape of its distribution is not as important.
I then develop my own agent-based model of the market. With just a few different
types of traders operating according to some simple rules, my model generates log returns
with many of the statistical properties found in empirical data. The option for traders
to opt out of trading is the source of the thin-peaked distribution of the simulated log
returns. The distribution of log returns becomes more closely described by a Gaussian at
longer lags. This is a consequence of basing the fundamental value of the stock on geometric
Brownian motion. Since transition to Gaussianity at long lags is also a feature of
empirical log returns, this implies that real traders are also influenced by some geometric
Brownian process. Log returns generated by the model also have volatility clustering, are
uncorrelated and asymmetrically distributed.
I test the log returns generated by my model for their scaling properties and find that
they do not have multifractal scaling. This is an interesting result since the simulated log
returns do feature other properties of empirical data. I then extend the model in some
basic ways to include more heterogeneity. Some limited multifractal scaling is found in
the simulated log returns of the extended model. Because the model produces stochastic
output, it is extremely difficult to exactly determine the scaling properties. However the
results hint at the possibility that the multifractality found in empirical log returns is a
consequence of the heterogeneity in both the investment horizons and beliefs of traders
in the market.
Item Type: | Thesis (PhD) |
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Keywords: | Financial Logarithmic Return Data; Multifractal and Agent-Based Techniques; |
Academic Unit: | Faculty of Science and Engineering > Mathematical Physics |
Item ID: | 6190 |
Depositing User: | IR eTheses |
Date Deposited: | 11 Jun 2015 14:21 |
URI: | https://mu.eprints-hosting.org/id/eprint/6190 |
Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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