Online Prediction Methods for Nonstationary Time Series

We present online prediction methods for univariate and multivariate time series models that allow us to factor in nonstationary artifacts present in many real time series. Specifically, we show that applying appropriate transformations to such time series can lead to improved theoretical and empirical prediction performance. In the univariate case this allows for seasonality and other trends in the time series, but to deal with the phenomenon of cointegration in multivariate time series, we present a novel algorithm denoted EC-VARMA-OGD. Our algorithms and regret analysis subsumes recent related work while significantly expanding the domain of 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 transformation, 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.