The analysis of crisis influence on the cross-correlation of the foreign exchange market (forex) daily exchange rates time series is presented. The analysis was conducted on 42 exchange rates with PLN as the common base currency. The time series cover the period from 09.10.2007 till 08.08.2015. Cross-correlation of the time series was analysed by power law classification scheme. It was shown that the strength of correlation allows not only to properly distinguish crisis and prosperity periods but also, followed by network analysis, is capable of recognizing the nodes which are the source of the crisis.
A new algorithm of the analysis of correlation among economy time series is proposed. The algorithm is based on the power law classification scheme followed by the analysis of the network on the percolation threshold. The algorithm was applied to the analysis of correlations among gross domestic product per capita time series of 19 most developed countries in the periods (1982, 2011), (1992, 2011) and (2002, 2011). The representative countries with respect to strength of correlation, convergence of time series and stability of correlation are distinguished. The results are compared with ultrametric distance matrix analysed by network on the percolation threshold.
Standard analysis of correlations between companies consists of two stages: calculating the distance matrix and construction of a chosen graph structure. In the paper the most often used Ultrametric Distance (UD) is compared with the Manhattan Distance (MD). It is showed that MD allows to investigate a broader class of correlation and is more robust to the noise influence. Therefore MD was used to construct entropy distance, which is applied to the analysis of correlation between subset of WIG20 and S&P500 companies. In the analysis three network structures were used: minimum spanning tree and unidirectional and bidirectional minimum length path. The results are compared to the standard UD based analysis. The advantages and disadvantages of the analysed time series distances are outlined.
Cross-correlations among the chosen six main world financial markets are analysed by power law classification scheme (PLCS). The markets are represented by indices: DAX (Frankfurt), FTSE (London), S&P 500 (New York), HSI (Honkong), Nikkei 225 (Tokyo), STI (Singapore) in the interval from 24.09.1991 till 31.01.2014. The time series are transformed into daily returns and normalised daily range of indices. The evolution of correlation strength is analysed using moving time window. It is shown that the correlation strength properly characterises crisis and prosperity periods. Moreover, the value of the correlation strength can be related to the crisis severity. The results are compared with standard ultrametric distance based on Pearson coefficient.
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