The aim of this study is to test the Fractal Market Hypothesis with the Markov regime change model in the Tehran Stock Exchange.One of the concepts in the efficient market is whether the financial time series has long-term memory and fractal properties or not. Given the characteristics of the capital market, which is always faced with random shocks and leads to fluctuations in this market, it is necessary to examine the fractal characteristics of the market.In this paper, the amount of long-term memory and stability of financial time series resulting from the total stock market index for the period 2009-2019 were examined. For this purpose, first, the existence of long-term memory was examined, and then the fractal nature of the market was examined using the Harst view index. The results indicate the existence of long-term memory in this variable. In this case, with one differentiation, it becomes more differentiated, so the stock price index series in Iran has long-term memory and the effects of each shock on this variable due to its long-term memory remain for long periods. The results also showed that the overall stock market index is fractal.
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