SUMMARY
The paper discovers certain aspects of financial time series, in particular, modeling of return on assets. The object of research is a system of indicators for analyzing the returns of financial time series. There is a key feature that distinguishes the analysis of financial time series from the analysis of other time series, as financial theory and its empirical time series contain an element of uncertainty. As a result of this additional uncertainty, statistical theory and its methods and models play an important role in the analysis of financial time series.One of the most problematic places is the use of asset prices and their volatility in the analysis and forecasting of financial time series, which is false because such series contain an element of uncertainty. Therefore, the so-called return on financial assets and instruments should be used in tasks of this type.The paper deals with the types of return on financial assets that can be used in mathematical modeling and forecasting of stock indices. Static methods are used to eliminate the disadvantages of using financial asset prices in the analysis and forecasting of financial time series. The empirical properties of financial time series are examined using the PFTS (First Stock Trading System) and S&P 500 indices.A comprehensive system of indicators of time series analysis of financial assets is obtained. The proposed system involves the use of numerous methods of calculating the profitability (return) of assets in order to determine significant statistical characteristics of the data. Compared to similarly known methods of using prices (rather than profitability) of assets, this provides a key advantage that allows elements of uncertainty in financial and economic data.