Investing in stock indexes has become an integral part of financial portfolios. Fearing the loss of savings value, households move their financial reserves into stocks, bonds and stock indexes; the latest concerns the subject of this article. The article focuses on determining the best method of forecasting the prices of stock indexes, S&P 500 and NASDAQ Composite, comparing the Simple moving average (SMA) technique with the Autoregressive integrated moving average (ARIMA) model based on free software RStudio. We formulated two plausible hypotheses: Which of these two methods -SMA or ARIMA -is more accurate for predicting the prices of selected stock indexes in the last thirty years? How will the price of the selected stock indexes develop according to the better of the suggested method through 2022? The ARIMA model indicated better results, proving great ability to forecast both indexes through 2022. The method determined the NASDAQ Composite stock index value to be 16,115.75 USD per stock through 31.12.2022, whereas S&P 500 index saw the value of 5,025.86 USD per stock through the same date. The follow-up research should deal with forecasting different stock indexes and comparing other conventional techniques for predicting time series. The subsequent study may also compare methods' forecasting accuracy between stock indexes and independent companies, whose stock volatility could favour different forecasting approaches.