# STR: Seasonal-Trend Decomposition Using Regression

arXiv: https://arxiv.org/abs/2009.05894 · HTML: https://mlsanity.com/paper/2009.05894/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2020.

## Built on by (most cited first, 9 of 9)

- [Time Series Analysis in Frequency Domain: A Survey of Open Challenges, Opportunities and Benchmarks](https://mlsanity.com/paper/2504.07099/) (2025)
- [OnlineSTL: Scaling Time Series Decomposition by 100x](https://mlsanity.com/paper/2107.09110/) (2021)
- [STD: A Seasonal-Trend-Dispersion Decomposition of Time Series](https://mlsanity.com/paper/2204.10398/) (2022)
- [Respecting Time Series Properties Makes Deep Time Series Forecasting Perfect](https://mlsanity.com/paper/2207.10941/) (2022)
- [Conformal time series decomposition with component-wise exchangeability](https://mlsanity.com/paper/2406.16766/) (2024)
- [Preserving Seasonal and Trend Information: A Variational Autoencoder-Latent Space Arithmetic Based Approach for Non-stationary Learning](https://mlsanity.com/paper/2504.18819/) (2025)
- [Improving Accuracy Without Losing Interpretability: A ML Approach for Time Series Forecasting](https://mlsanity.com/paper/2212.06620/) (2022)
- [Long-term foehn reconstruction combining unsupervised and supervised learning](https://mlsanity.com/paper/2406.01818/) (2024)
- [Frequency-Aware Attention-LSTM for PM2.5 Time Series Forecasting](https://mlsanity.com/paper/2503.24043/) (2025)

## Abstract (arXiv)

We propose a new method for decomposing seasonal data: STR (a Seasonal-Trend decomposition using Regression). Unlike other decomposition methods, STR allows for multiple seasonal and cyclic components, covariates, seasonal patterns that may have non-integer periods, and seasonality with complex topology. It can be used for time series with any regular time index including hourly, daily, weekly, monthly or quarterly data. It is competitive with existing methods when they exist, but tackles many more decomposition problem than other methods allow. STR is based on a regularized optimization, and so is somewhat related to ridge regression. Because it is based on a statistical model, we can easily compute confidence intervals for components, something that is not possible with most existing decomposition methods (such as STL, X-12-ARIMA, SEATS-TRAMO, etc.). Our model is implemented in the R package stR, so can be applied by anyone to their own data.