The research aims to use the Dynamic Equality Condition Correlation (DECO-GARCH) model to test the general movements and conditional relationships regarding the return on investment in a financial market. This is distinguished from other models, particularly from the DCC model, as it is based on calculating the pairwise correlations of assets (joint return volatilities) at one time for all assets, while relying on the history of those assets. This study focused on the returns of US stock market indices, the Chinese stock market index, and financial markets in some Middle Eastern countries, (S&P 500, DJI, NASDAQ Composite, Shanghai Composite, Saudi General, Dubai General, Bahrain General, Amman General, Iraq Stock Exchange). We conduct this research on the grounds of understanding the impact of financial crises on asset returns in these markets, the interconnections that govern them, and the extent to which investors can hedge their investments in these markets. The results have revealed significant and varying correlations between these indices, with increased equal relationships observed in 2015–2016 and 2020–2021, which corresponding to the dates of the European debt crisis, the collapse of the Chinese stock market, and the COVID-19 pandemic. Overall, there was noticeable fluctuation in the conditional dynamic equality among the studied indices during the study period, thus supporting the hypothesis of contagion effects and emphasizing the importance of considering the evolving nature of relationships between these indices when making asset allocation decisions.
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