Network Analysis of Correlation Strength between the Most Developed Countries

Abstract

A new algorithm of the analysis of correlation among economy time series is proposed. The algorithm is based on the power law classication 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.

Cross-Correlations of the Forex Market Using Power Law Classification Scheme Picture

“…According to observation made in previous analyses [11,12,17,18] two time window sizes were chosen: T =50 d (d) and T = 100 d. The analysis was conducted using overlapping time windows, so the time window was shifted by one day at each step and the PLCS algorithm applied. Since the log-return time series consisted of 1999 data points the moving time window technique transformed it into 1950 correlation strength matrices for T = 50 d and 1900 for T = 100 d. Moreover, each of the matrices consists of 861 independent elements above (or below) diagonal.…”

“…The method was introduced in [11] and later developed in [12] and [17]. Although the detailed description of the algorithm can be found in [11,12,17], for the convenience of the reader the main steps of PLCS are recalled also here. The algorithm is based on the Manhattan distance.…”

“…For the strength preferential network, the nodes are connected when their correlation strength is greater than zero, which can be interpreted as diverging time series so the differences between the considered time series are increasing. The increase of differences among times indicates usually a crisis, particularly when it is observed at the same time between several nodes [11,12,17,18]. Analysing the crisis level one usually looks for the set of the most affected nodes.…”

“…become a subject of interest of econophysicists, who were developing methods of cross-correlation analysis e.g. [8][9][10][11][12]. The recently developed methods can be grouped into three main branches.…”

“…The second group of methods are the algorithms originated in DFA such that MF-CCA [8,16]. The third set, very promising, are the Manhattan distance based algorithms -the entropy analysis [6,7] and the power low classification scheme (PLCS) [11,12,17,18]. The later method allows measuring the strength and stability of correlations.…”