In this paper we have studied DMD method used to approximate nonlinear dynamics system solution. We analyze the theoretical background, intuitive interpretation and a numerical algorithm. We also describe the POD method which appears in the background of the DMD algorithm. We emphasize the importance of the SVD matrix decomposition which gives us POD modes and the generalized inverse matrix. POD method finds, in terms of least squares, the best subspace for a given set of vectors. Such a subspace is suitable for the approximation of a higher ranking system with a lower ranking system. The DMD method finds coherent spatio-temporal modes that form the motion. They are given by the eigenvectors of the matrix \(A\) that describes the locally linearized dynamics of the system. The mapping operator \(A\) is generally unknown, but we know the measured system states that are sufficient for the reconstruction of the dynamics. We can determine the operator \(\tilde{A}\) (lower rank approximation of \(A\)) using only measured states. The eigenvalues of the operator \(\tilde{A}\) are a subset of the eigenvalues of the operator \(A\), and from the eignevectors of operator \(\tilde{A}\) we easily reconstruct the corresponding eigenvectors of operator \(A\). That eignevectors are called DMD modes. The proximal state of the system is obtained from DMD modes, associated eigenvalues and initial states. We apply the DMD method to stock prices. We capture the dynamics of price movements and predict where the price will go in the next few moments. Using that forecasting, we develop an investment strategy and ultimately get a successful method of algorithmic trading. In the last chapter we put the DMD method into a broader theoretical context. We introduce the Koopman operator and describe the EDMD method by which we calculate eigenvalues, eigenfunctions and modes of Koopman operator. We show the link between the DMD algorithm and the EDMD algorithm and we conclude that DMD method is only a special case of EDMD method.