This paper deals with the development of a method for predicting the trajectory of a pseudo-stationary fragment of the economic cycle. The latter is represented by discrete values (readouts) of random oscillations of the income function. The statistical equivalence of these readouts and second-order autoregression (Yule series) led to the adaptation of the autoregressive model to the specified fragment of the cycle. It is proposed to use the adapted autoregressive model as a tool for predicting cycle values via the method of statistical tests (Monte-Carlo) by forming the most probable cycle trajectory. The procedure for the formation of the cycle trajectory is described in detail and its parameters have formal justifications. The content of the subsequent statistical analysis of the simulation results is illustrated by the example of determining the instant of the predicted peak value of the cycle. The presented method is applicable in macroeconomic and econometric problems, the solution to which requires knowledge of the predicted trajectory of the cycle under consideration.