WARMA: A Window-Based Autoregressive Moving Average Model for Non-Stationary Time Series

• Arthur Ronald Garcia Centro Federal de Educação Tecnológica Celso Suckow da Fonseca (CEFET/RJ)
• Jorge Soares Centro Federal de Educação Tecnológica Celso Suckow da Fonseca (CEFET/RJ) https://orcid.org/0000-0001-6772-9099
• Laura Assis Centro Federal de Educação Tecnológica Celso Suckow da Fonseca (CEFET/RJ)
• Fabio Porto Laboratório Nacional de Computação Científica (LNCC)
• Dayse Pastore Centro Federal de Educação Tecnológica Celso Suckow da Fonseca (CEFET/RJ)
• Eduardo Ogasawara Centro Federal de Educação Tecnológica Celso Suckow da Fonseca (CEFET/RJ)

DOI: https://doi.org/10.5753/sbbd.2026.249335

Resumo

Many time-series models assume stationarity. Analysts therefore often apply global transformations such as differencing. Although these transformations can be effective, they also change the mean, variance, and covariance simultaneously, making the original series harder to interpret. We present WARMA, a model that combines window-based preprocessing with ARMA modeling. The model operates locally over sliding windows. WARMA first adjusts the mean and then the variance, so the preprocessing remains interpretable in terms of steps. Experiments on synthetic and real economic-financial series show that WARMA reaches stationarity in at most two steps and delivers forecasting accuracy comparable to that of ARIMA while providing a more localized view of the preprocessing effect.

Palavras-chave: Non-Stationary Time Series, Autoregressive Moving Average Models, Window-Based Preprocessing, Local Stationarization, Time Series Forecasting

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