Time series decomposition plays an important role in time series analysis, anomaly detection, and forecasting, with significant applications in big data mining. However, current research on time series decomposition faces challenges in real-time processing, accuracy, and applicability. This paper proposes an online seasonal-trend decomposition (STD) algorithm, the \(\alpha \) -STD algorithm, which is based on an additive time series decomposition model, and extends it to multi-seasonal scenarios. An adaptive scaling component \(\alpha \) is introduced to capture trend variations through periodic differencing of normalized time series values. By incorporating \(\alpha \) as a dynamic scaling factor for seasonal components, our algorithm effectively models the multiplicative relationships between trends and seasonality within a traditional additive decomposition model. The \(\alpha \) -STD algorithm demonstrates superior performance in handling time series with trend jumps, seasonal shifts, and heteroscedasticity while maintaining an \(\mathcal {O}(1)\) update complexity. Furthermore, this paper provides solutions for handling missing data in online time series decomposition. The experimental results indicate that the \(\alpha \) -STD has broader applicability than baseline methods do, achieving high decomposition accuracy across various datasets and effectively mitigating the impact of missing data on online decomposition tasks.