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In this paper, a new approach is proposed for the system identification of the stock returns. Allocating an accurate model to the nonlinear and stochastic financial system, which can accurately manifest the system, is considered one of the critical issues in control and system engineering. We employ an autoregressive with exogenous variable (ARX) process and propose a new model that accurately exhibits the stock returns system dynamics. The proposed model can identify the system with more than 96% accuracy. Furthermore, one of the indispensable approaches in the financial market, which presents a significant investment role, is forecasting the trends accurately. Therefore, we propose and implement a new algorithm, multiple adaptive forecast (MAF), based on adaptive control systems, estimation, and stochastic processes to detect the future trends of prices. In addition, we study some companies' stocks from Tehran Stock Exchange in this paper. Simulation results indicate that the proposed model obtains more accurate outcomes than the two other models. Ultimately, as inferred from the simulation results, employing the proposed model combined with the MAF algorithm would yield more competent outcomes for creating the portfolio for short-term investment. [ABSTRACT FROM AUTHOR]