Period Estimation For Incomplete Time Series

Natural and human-engineered systems often exhibit periodic behavior. Examples include the climate system, migration of animals in the wild, consumption of electricity in the power grid and others. The behavior of such systems, however, is not perfectly periodic. The time series we collect from them are often noisy and incomplete due to limitations of data collection and transmission, or due to sensor malfunction and outages. In addition, there are often multiple periods, for example, air temperature and pressure oscillates daily and yearly with the seasons. Hence, accurate and robust period estimation from raw time series is a fundamental task often employed in downstream applications such as traffic prediction and anomaly detection. In this paper, we study the period estimation problem in noisy time series with multiple periods and missing values. We propose a method based on a Ramanujan periodic dictionary and a vector completion model to estimate missing values. To account for the block structure in the Ramanujan periodic dictionary, we introduce a graph Laplacian group lasso regularization which enables robust and efficient period learning in the presence of missing observations. In our extensive experiments on datasets from diverse domains, our proposed methodology outperforms state-of-art baselines in terms of accuracy of period estimation.