Multi-fluctuation nonlinear patterns of European financial markets based on adaptive filtering with application to family business, green, Islamic, common stocks, and comparison with Bitcoin, NASDAQ, and VIX

Abstract

This paper investigates power-law correlations, chaos, and randomness in prices of family business, green (low Carbon), Islamic (Shariah), and common stock indices from the European zone. Specifically, the estimations of nonlinear patterns are performed in empirical mode decomposition domain to obtain time-scale computed values. The main findings follow. For all markets, price long term fluctuations are persistent, whilst price short term fluctuations are anti-persistent. In addition, short term fluctuations are chaotic, while long term fluctuations are not. Furthermore, short term fluctuations are less affected by randomness than long term fluctuations. Moreover, the level of anti-persistence and the information content in short term fluctuations are similar across all four European markets. Besides, computed nonlinear statistics from intermediate fluctuations are in general lower than those from short fluctuations, and are higher than those from long fluctuations. Our methodology is also applied to Bitcoin, NASDAQ, and VIX indices for comparison purpose. Some similarities in terms of randomness and dissimilarities in terms of long memory are clearly observed between European and US indices. Finally, it is found that the correlation between (i) long memory and chaos is positive, low, and not statistically significant, (ii) between long memory and randomness is positive, large, and statistically significant, and (iii) between chaos and randomness is negative, low, and not statistically significant. Active traders and portfolio managers can follow our research approach to determine specific trading strategies at short and long run horizons.