NonSTOP: A NonSTationary Online Prediction Method for Time Series
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We present online prediction methods for univariate and multivariate time series that allow us to handle nonstationary artifacts present in most real time series. Specifically, we show that applying appropriate transformations to such time series can lead to improved theoretical and empirical prediction performance. Moreover, since these transformations are usually unknown, we employ the learning with experts setting to develop a fully online method (NonSTOP) for predicting nonstationary time series. This framework allows for seasonality and/or other trends in univariate time series and cointegration in multivariate time series. Our algorithms and regret analysis subsumes recent related work while significantly expanding the applicability of such methods. For all the methods, we provide sub-linear regret bounds using relaxed assumptions. We note that the theoretical guarantees do not fully capture the benefits of the nonstationary transformations, thus we provide a data-dependent analysis of the follow-the-leader algorithm for least squares loss that provides insight into the success of using nonstationary transformations. We support all of our results with experiments on simulated and real data.
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