Learning Periods from Incomplete Multivariate Time Series
Lin Zhang, Alexander Gorovits, Wenyu Zhang, Petko Bogdanov · 2020
Modeling and detection of seasonality in time series is essential for accurate analysis, prediction and anomaly detection. Examples of seasonal effects at different scales abound: the increase in consumer product sales during the holiday season recurs yearly, and similarly household electricity usage has daily, weekly and yearly cycles. The period in real-world time series, however, may be obfuscated by noise and missing values arising in data acquisition. How can one learn the natural periodicity from incomplete multivariate time series? We propose a robust framework for multivariate period detection, called LAPIS. It encodes incomplete and noisy data as a sparse summary via a Ramanujan periodic dictionary. LAPIS can accurately detect a mixture of multiple periods in the same time series even when 70% of the observations are missing. A key innovation of our framework is that it exploits shared periods across individual time series even when they are not correlated or in-phase. Beyond detecting periods, LAPIS enables improvements in downstream applications such as forecasting, missing value imputation and clustering. At the same time our approach scales to large real-world data executing within seconds on datasets of length up to half a million time points.