Comparative Analysis of the Implementation of Classical Statistical Models for Univariate Time Series Forecasting in Python, R, and Julia

Abstract

This study presents a comparative analysis of the implementation of classical statistical models for univariate time series forecasting in the programming environments Python, R, and Julia. The research examines naïve and seasonal naïve methods, exponential smoothing (ETS), as well as the automatic parameter selection of autoregressive integrated moving average models (Auto-ARIMA). Two datasets were used for the experiments: daily Brent crude oil prices and monthly average wage indicators in Ukraine. Forecast accuracy was evaluated using three metrics — RMSE, MASE, and sMAPE — across different forecasting horizons. The results demonstrate that modeling outcomes depend not only on the mathematical nature of the algorithms but also on the specifics of their implementation in the respective ecosystems. It was found that Python and R provide full support for all the models under consideration, whereas Julia, at the time of the study, lacked stable implementations of ETS and Auto-ARIMA, which partially limited the possibilities for comparison. The findings are relevant both for assessing the maturity of software ecosystems in the field of time series analysis and for guiding the practical selection of tools in applied forecasting tasks.