Learning Time Series from Scale Information

TL;DR

This paper introduces a scale-based inference approach for time series, leveraging multi-resolution data to improve prediction accuracy through a novel algorithm and theoretical guarantees.

Contribution

It proposes a new scale inference method for time series that combines multi-resolution data, with theoretical analysis and practical algorithms for improved predictions.

Findings

The algorithm asymptotically matches the best single-resolution predictor.

The approach is effective on both synthetic and real datasets.

The method provides a unified framework for scale-aware time series prediction.

Abstract

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.