Evaluating and study of the Fractal Properties of Capital Markets Based on DE trended Fluctuation Analysis (Case Study: Exchange Market and Stock Index of Tehran)

In this study, the long-term memory of the stock market index and exchange rate (dollar) was estimated using detrended fluctuation analysis. In order to detrend the data, the GARCH approach was proposed and the long-term memory estimation model was implemented separately for both conventional and GARCH methods. For this purpose, daily data of stock market index and dollar exchange rate in the market during the years 2014 to 2020 were used. The results showed that the conventional method in calculating the detrended fluctuations is not able to estimate the long-term memory of the exchange rate, while the results for the stock index showed the existence of short-term memory. The results showed that the proposed method in detrending data and calculating detrended fluctuations based on Garch model has a higher power in controlling changes in market fluctuations and according to the findings of this method, stock index and dollar exchange rate have long-term memory. The results showed that these two methods provide significantly different estimates of long-term memory of the market and according to the results of the correlation test between the values ​​of long-term memory of data and the value of parameter q in detrended fluctuation analysis; it was observed that the stock market index and exchange rate in Iran have multifractal properties.