STR: Seasonal-Trend Decomposition Using Regression

TL;DR

STR is a flexible and comprehensive seasonal-trend decomposition method that handles multiple seasonalities, covariates, and complex patterns, providing confidence intervals and broad applicability across various time series data.

Contribution

It introduces a new regression-based decomposition method capable of modeling complex seasonal patterns and multiple components, with statistical inference features.

Findings

Handles multiple seasonal and cyclic components

Provides confidence intervals for decomposed components

Applicable to diverse regular time series data

Abstract

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.