Learning Time Series from Scale Information
This work addresses the challenge of improving time series prediction accuracy for applications where data exhibits different behaviors at different scales, offering a novel inference framework that is incremental in its methodological advancement.
The paper tackles the problem of predicting time series by leveraging scale information, such as resolution or sampling rate, and proposes a scale-based inference approach that uses data from multiple resolutions. The result is an algorithm that asymptotically achieves a mean prediction error no larger than the best possible algorithm at any single resolution, with experiments showing applicability across various time series models.
Sequentially obtained dataset usually exhibits different behavior at different data resolutions/scales. Instead of inferring from data at each scale individually, it is often more informative to interpret the data as an ensemble of time series from different scales. This naturally motivated us to propose a new concept referred to as the scale-based inference. The basic idea is that more accurate prediction can be made by exploiting scale information of a time series. We first propose a nonparametric predictor based on $k$-nearest neighbors with an optimally chosen $k$ for a single time series. Based on that, we focus on a specific but important type of scale information, the resolution/sampling rate of time series data. We then propose an algorithm to sequentially predict time series using past data at various resolutions. We prove that asymptotically the algorithm produces the mean prediction error that is no larger than the best possible algorithm at any single resolution, under some optimally chosen parameters. Finally, we establish the general formulations for scale inference, and provide further motivating examples. Experiments on both synthetic and real data illustrate the potential applicability of our approaches to a wide range of time series models.