This paper proposes methods of predicting dynamic time series (including non-stationary ones) based on a linguistic approach, namely, the study of occurrences and repetition of so-called N-grams. This approach is used in computational linguistics to create statistical translators, detect plagiarism and duplicate documents. However, the scope of application can be extended beyond linguistics by taking into account the correlations of sequences of stable word combinations, as well as trends. The proposed methods do not require a preliminary study and determination of the characteristics of time series or complex tuning of the input parameters of the forecasting model. They allow, with a high level of automation, to carry out short-term and medium-term forecasts of time series, characterized by trends and cyclicality, in particular, series of publication dynamics in content monitoring systems. Also, the proposed methods can be used to predict the values of the parameters of a large complex system with the aim of monitoring its state, when the number of such parameters is significant, and therefore a high level of automation of the forecasting process is desirable. A significant advantage of the approach is the absence of requirements for time series stationarity and a small number of tuning parameters. Further research may focus on the study of various criteria for the similarity of time series fragments, the use of nonlinear similarity criteria, the search for ways to automatically determine the rational step of quantization of the time series.