Arash Azariyoon - Ph.D. student of industrial management, Roodehen branch, Islamic azad university, Roodehen, Iran.
narges yazdanian - Assistant professor of accounting, Accounting department, Roodehen branch, Islamic azad university, Roodehen, Iran.
Alireza Mirarab - Assistant professor of accounting, Accounting department, Roodehen branch, Islamic azad university, Roodehen, Iran.
Hoda Hemmati - Assistant professor of accounting, Accounting department, Roodehen branch, Islamic azad university, Roodehen, Iran.

In this study, the relationship between stock market long-term memory and exchange rate was studied. For this purpose, the analysis of detrended fluctuations was used and in order to detrend the data, two common detrending methods and cross-detrending were used. The research data included daily information of the stock market index and the dollar exchange rate during the period ۲۰۱۴/۰۳/۲۵ to ۲۰۲۱/۰۲/۰۷ and the data analysis was performed using the regression models. The results showed that the cross-trending of parallel markets produces different results in estimating the long-term memory of the data. According to the research findings, the stock index has a short-term memory under the conventional detrending method, while the cross-detrending method shows long-term memory for this index. The results for the exchange rate showed that under the conventional detrending method, the long-term memory of the exchange rate cannot be estimated in all market volatilities situations, while the cross-detrending method showed that the exchange rate loses its long-term memory in the face of increasing market fluctuations. The results also showed that under the cross-trending method, there is a direct and significant relationship between the long-term memory of the stock market index and the exchange rate.

Detrended fluctuations, parallel markets, Cross detrending, long-term memory