Both classical forecasting methods and machine learning approaches are used to solve forecasting problems. Deep artificial neural networks, one of the machine learning methods, are widely used today and give very good results. Recurrent neural networks, a type of deep neural network, are very important in forecasting problems. Simple recurrent artificial neural networks, which are the simplest deep recurrent neural networks, are often preferred in solving forecasting problems due to the small number of parameters they use. Simple exponential smoothing, one of the classical forecasting methods, attracts attention with its performance in solving forecasting problems. The motivation of the study is to create a new forecasting method by combining a classical and simple forecasting method with a deep recurrent artificial neural network in an architecture. In this, a new hybrid deep recurrent artificial neural network with a simple exponential smoothing feedback mechanism is proposed. The architecture of the proposed method is created as a combination of simple recurrent artificial neural networks and simple exponential smoothing methods. In the training of the proposed method, two training algorithms based on sine cosine optimization and particle swarm optimization algorithms are proposed. In these training algorithms, two different solution strategies such as restarting, and early stopping rule are used to avoid overfitting and local optimum problems. The performance of the proposed method is analysed using stock market datasets and compared with both different deep and shallow artificial neural networks and classical forecasting methods. As a result of the analyses, it is concluded that the proposed method is successful in one step ahead of forecasting performance.