The article focuses on the development of the dynamic-stochastic approach (DSA) to mathematical modeling. As an example, we consider the modeling of competitive interaction between two passenger car manufacturers — Audi and BMW. We used the data on annual car sales from 2005 to 2020. We examine possible variants of dynamic models that have linear parameters: the Volterra model and a system of linear differential equations. Each dynamic model corresponds to a system of linear regression equations. The parameters of these regression equations are estimated using the OLS (Ordinary Least Squares) method. The final selection of the dynamic model is based on the F-test. Based on the selected model (Volterra model), we calculate the covariance matrix of OLS-estimates of the parameter vector of the centered regression model for independent responses. We use this matrix to get the covariance matrix of the dynamic model parameter vector. Following the DSA, we use the Monte Carlo method to add perturbations to all parameters of the dynamic model, according to their distribution. We calculate an ensemble of integrations, which is used to forecast the number of sales for 5 years ahead in terms of ensemble averages and confidence intervals. We also can calculate the probabilities of different situations in the future.