In this study we show that standard well-known file compression programs (zlib, bzip2, etc.) are able to forecast real-world time series data well. The strength of our approach is its ability to use a set of data compression algorithms and "automatically" choose the best one of them during the process of forecasting. Besides, modern data-compressors are able to find many kinds of latent regularities using some methods of artificial intelligence (for example, some data-compressors are based on finding the smallest formal grammar that describes the time series). Thus, our approach makes it possible to apply some particular methods of artificial intelligence for time-series forecasting. As examples of the application of the proposed method, we made forecasts for the monthly T-index and the Kp-index time series using standard compressors. In both cases, we used the Mean Absolute Error (MAE) as an accuracy measure. For the monthly T-index time series, we made 18 forecasts beyond the available data for each month since January 2011 to July 2017. We show that, in comparison with the forecasts made by the Australian Bureau of Meteorology, our method more accurately predicts one value ahead. The Kp-index time series consists of 3-hour values ranging from 0 to 9. For each day from February 4, 2018 to March 28, 2018, we made forecasts for 24 values ahead. We compared our forecasts with the forecasts made by the Space Weather Prediction Center (SWPC). The results showed that the accuracy of our method is similar to the accuracy of the SWPC's method. As in the previous case, we also obtained more accurate one-step forecasts.