The article is devoted to a comparative analysis of the use of adaptive methods and models, autoregressive models and neural networks in forecasting the exchange rate of the main reserve currencies: the euro, the Swiss franc, the Japanese yen and the British pound against the US dollar. In the course of the research, the works of Ukrainian and foreign scientists on this topic were reviewed and it was determined that the most used methods and models in forecasting the exchange rate based on time series are autoregression models (represented by ARIMA and SARIMA models), neural networks (represented by MLP and ELM architectures) and exponential smoothing methods. In the process of building the models, time series were examined for stationarity based on the Dickey-Fuller test and additive decomposition of the studied time series was performed to determine their main components (trend, seasonality, random component). Construction of forecast models was carried out, on the basis of which their comparative analysis took place. The main shortcomings and problems of using the selected methods are demonstrated and the best predictive models are determined. It is determined that the main drawback of all time series forecasting methods is their "adaptability" to the input data, and the desire to improve the estimation characteristics of the models as a result can lead to the fact that the forecasts differ significantly from the actual values. It was also determined that for forecasting the exchange rate of selected currency pairs, neural networks are best suited, which have both high evaluation characteristics and correspondence of the forecast to real values, and the MLP network shows better results compared to the ELM network. High evaluation characteristics are also demonstrated by adaptive models. However, the linear nature of the forecast does not allow adaptive models to make an accurate forecast in the long term. Although autoregressive models show worse estimation characteristics, they outperform neural networks in terms of matching real values for individual currency pairs.