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Register a new userDetrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces
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Authors
Xi-Yuan Qian
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When common factors strongly influence two power-law cross-correlated time series recorded in complex natural or social systems, using classic detrended cross-correlation analysis (DCCA) without considering these common factors will bias the results. We use detrended partial cross-correlation analysis (DPXA) to uncover the intrinsic power-law cross-correlations between two simultaneously recorded time series in the presence of nonstationarity after removing the effects of other time series acting as common forces. The DPXA method is a generalization of the detrended cross-correlation analysis that takes into account partial correlation analysis. We demonstrate the method by using bivariate fractional Brownian motions contaminated with a fractional Brownian motion. We find that the DPXA is able to recover the analytical cross Hurst indices, and thus the multi-scale DPXA coefficients are a viable alternative to the conventional cross-correlation coefficient. We demonstrate the advantage of the DPXA coefficients over the DCCA coefficients by analyzing contaminated bivariate fractional Brownian motions. We calculate the DPXA coefficients and use them to extract the intrinsic cross-correlation between crude oil and gold futures by taking into consideration the impact of the US dollar index. We develop the multifractal DPXA (MF-DPXA) method in order to generalize the DPXA method and investigate multifractal time series. We analyze multifractal binomial measures masked with strong white noises and find that the MF-DPXA method quantifies the hidden multifractal nature while the MF-DCCA method fails.
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We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based multifractal formalism, and prove that both approaches are equivalent for stationary signals with compact support. By analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series. By comparing the multifractal DFA results for original series to those for shuffled series we can distinguish multifractality due to long-range correlations from multifractality due to a broad probability density function. We also compare our results with the wavelet transform modulus maxima (WTMM) method, and show that the results are equivalent.
The stock market has been known to form homogeneous stock groups with a higher correlation among different stocks according to common economic factors that influence individual stocks. We investigate the role of common economic factors in the market in the formation of stock networks, using the arbitrage pricing model reflecting essential properties of common economic factors. We find that the degree of consistency between real and model stock networks increases as additional common economic factors are incorporated into our model. Furthermore, we find that individual stocks with a large number of links to other stocks in a network are more highly correlated with common economic factors than those with a small number of links. This suggests that common economic factors in the stock market can be understood in terms of deterministic factors.
In this study, we have investigated factors of determination which can affect the connected structure of a stock network. The representative index for topological properties of a stock network is the number of links with other stocks. We used the multi-factor model, extensively acknowledged in financial literature. In the multi-factor model, common factors act as independent variables while returns of individual stocks act as dependent variables. We calculated the coefficient of determination, which represents the measurement value of the degree in which dependent variables are explained by independent variables. Therefore, we investigated the relationship between the number of links in the stock network and the coefficient of determination in the multi-factor model. We used individual stocks traded on the market indices of Korea, Japan, Canada, Italy and the UK. The results are as follows. We found that the mean coefficient of determination of stocks with a large number of links have higher values than those with a small number of links with other stocks. These results suggest that common factors are significantly deterministic factors to be taken into account when making a stock network. Furthermore, stocks with a large number of links to other stocks can be more affected by common factors.
We investigated the topological properties of stock networks through a comparison of the original stock network with the estimated stock network from the correlation matrix created by the random matrix theory (RMT). We used individual stocks traded on the market indices of Korea, Japan, Canada, the USA, Italy, and the UK. The results are as follows. As the correlation matrix reflects the more eigenvalue property, the estimated stock network from the correlation matrix gradually increases the degree of consistency with the original stock network. Each stock with a different number of links to other stocks in the original stock network shows a different response. In particular, the largest eigenvalue is a significant deterministic factor in terms of the formation of a stock network.
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