An alternative investment theory to the widely utilized efficient market hypothesis, fractal market hypothesis analyses the daily randomness of the market and the turbulence witnessed during crashes and crises. The framework of the fractal market hypothesis proposes a clear explanation of investor behaviour throughout a market cycle, including booms and busts. Nowadays, the importance and advantages of forecasting in decision and policy making from different dimensions are undeniably accepted. Naturally, the techniques that face the lowest forecasting errors are capable of survival and proper function. Successful structural models have not been recently employed in the field of forecasting; therefore, other tests have been proposed among which L‐Co‐R algorithm is the most notably known for time series analysis. The present study applies L‐Co‐R coevolutionary algorithm for forecasting and analysis of time series stock returns. The current study examines daily, monthly, and yearly time series stock returns on Tehran Stock Exchange and London Stock Exchange over a period from 2007 to 2013. The statistical analysis in London Stock Exchange shows that the L‐Co‐R algorithm outperforms to the other methods, regardless of the horizon, and is capable of predicting short, medium, or long horizons using real known values. The statistical analysis in Tehran Stock Exchange shows that the L‐Co‐R algorithm outperforms to the other methods and is capable of predicting only short and medium terms. Thus, fractal market hypothesis was accepted for Tehran Stock Exchange and rejected for London Stock Exchange.

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