| Summary: | This thesis discusses how properties of complex network theory can be used to study financial time series, in particular time series for stocks on the DAX 30. First, we make a comparison between three correlation-based networks: minimum spanning trees; assets graphs and planar maximally filtered graphs. A series of each of these network types is created for the same dataset of time series' of DAX 30 stocks and we consider what information each network can provide about the relationship between the stock prices from the underlying time series. We also analyse two specific time periods in further detail - a period of crisis and a period of recovery for the German economy. Next, we look at the structure and representations of planar maximally filtered graphs and in particular we consider the vertices that form the 3-cliques and 4-cliques [Tumminello et al. (2005)] state '... normalizing quantities are n_s - 3 for 4-cliques and 3n_s - 8 for 3-cliques. Although we lack a formal proof, our investigations suggest that these numbers are the maximal number of 4-cliques and 3-cliques, respectively, that can be observed in a PMFG of n_s elements.' Within this thesis we provide a proof for these quantities and a different construction algorithm. Finally, rather than correlation-based networks, we discuss two relatively new types of networks: visibility graphs and the geometrically simpler horizontal visibility graphs. We review the field's that these networks have already been applied to and consider if this is an appropriate method to apply to financial time series - specifically stock prices. We also consider using horizontal visibility graphs as a method for distinguishing between random and chaotic series within stock price time series.
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