SAZED: parameter-free domain-agnostic season length estimation in time series data

Season length estimation is the task of identifying the number of observations in the dominant repeating pattern of seasonal time series data. As such, it is a common pre-processing task crucial for various downstream applications. Inferring season length from a real-world time series is often challenging due to phenomena such as slightly varying period lengths and noise. These issues may, in turn, lead practitioners to dedicate considerable effort to preprocessing of time series data since existing approaches either require dedicated parameter-tuning or their performance is heavily domain-dependent. Hence, to address these challenges, we propose SAZED: spectral and average autocorrelation zero distance density. SAZED is a versatile ensemble of multiple, specialized time series season length estimation approaches. The combination of various base methods selected with respect to domain-agnostic criteria and a novel seasonality isolation technique, allow a broad applicability to real-world time series of varied properties. Further, SAZED is theoretically grounded and parameter-free, with a computational complexity of O(nlogn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}(n\log n)$$\end{document}, which makes it applicable in practice. In our experiments, SAZED was statistically significantly better than every other method on at least one dataset. The datasets we used for the evaluation consist of time series data from various real-world domains, sterile synthetic test cases and synthetic data that were designed to be seasonal and yet have no finite statistical moments of any order.