ﻻ يوجد ملخص باللغة العربية
We propose a modified time lag random matrix theory in order to study time lag cross-correlations in multiple time series. We apply the method to 48 world indices, one for each of 48 different countries. We find long-range power-law cross-correlations in the absolute values of returns that quantify risk, and find that they decay much more slowly than cross-correlations between the returns. The magnitude of the cross-correlations constitute bad news for international investment managers who may believe that risk is reduced by diversifying across countries. We find that when a market shock is transmitted around the world, the risk decays very slowly. We explain these time lag cross-correlations by introducing a global factor model (GFM) in which all index returns fluctuate in response to a single global factor. For each pair of individual time series of returns, the cross-correlations between returns (or magnitudes) can be modeled with the auto-correlations of the global factor returns (or magnitudes). We estimate the global factor using principal component analysis, which minimizes the variance of the residuals after removing the global trend. Using random matrix theory, a significant fraction of the world index cross-correlations can be explained by the global factor, which supports the utility of the GFM. We demonstrate applications of the GFM in forecasting risks at the world level, and in finding uncorrelated individual indices. We find 10 indices are practically uncorrelated with the global factor and with the remainder of the world indices, which is relevant information for world managers in reducing their portfolio risk. Finally, we argue that this general method can be applied to a wide range of phenomena in which time series are measured, ranging from seismology and physiology to atmospheric geophysics.
World currency network constitutes one of the most complex structures that is associated with the contemporary civilization. On a way towards quantifying its characteristics we study the cross correlations in changes of the daily foreign exchange rat
Using transfer entropy, we observed the strength and direction of information flow between stock indices. We uncovered that the biggest source of information flow is America. In contrast, the Asia/Pacific region the biggest is receives the most infor
A method for estimating the cross-correlation $C_{xy}(tau)$ of long-range correlated series $x(t)$ and $y(t)$, at varying lags $tau$ and scales $n$, is proposed. For fractional Brownian motions with Hurst exponents $H_1$ and $H_2$, the asymptotic exp
This paper analyzes correlations in patterns of trading of different members of the London Stock Exchange. The collection of strategies associated with a member institution is defined by the sequence of signs of net volume traded by that institution
Forecasting stock returns is a challenging problem due to the highly stochastic nature of the market and the vast array of factors and events that can influence trading volume and prices. Nevertheless it has proven to be an attractive target for mach