From classical to generative AI approaches for univariate and multivariate time series forecasting with an evaluation in finance, energy, and health domains

Time series forecasting plays a central role in finance, energy, and public health. Classical statistical, machine learning, deep learning, and generative approaches have all been applied to forecasting tasks in these fields, but comparisons between them are usually confined to a single domain or to models from the same family, and few studies report both univariate and multivariate results under the same conditions. This paper presents a controlled cross-domain comparison of four representative paradigms: classical statistics (Seasonal Autoregressive Integrated Moving Average with Exogenous variables, SARIMAX), gradient boosting machine learning (Light Gradient Boosting Machine, LightGBM), recurrent deep learning (Recurrent Neural Network, RNN), and generative-adversarial deep learning (Conditional Generative Adversarial Network, CGAN). Each model is evaluated on three monthly datasets with contrasting characteristics: Bitcoin prices (175 observations, high volatility), U.S. energy consumption (612 observations, strong seasonality), and U.S. cardiovascular mortality (300 observations, gradual trend with pandemic shock). Both univariate and multivariate variants are tested under the same preprocessing and one-step-ahead evaluation protocols, using eight performance metrics. The CGAN reaches the lowest MAPE on energy consumption (2.88%). On Bitcoin, the multivariate LightGBM lowers the MAPE from 28.26 to 19.25%, while on cardiovascular mortality the RNN reaches 3.34% MAPE. No paradigm performs best in every domain, and the gain from exogenous variables depends on both the paradigm and the domain.