We present online prediction methods for univariate and multivariate timeseries models that allow us to factor in nonstationary artifacts present inmany real time series. Specifically, we show that applying appropriatetransformations to such time series can lead to improved theoretical andempirical prediction performance. In the univariate case this allows forseasonality and other trends in the time series, but to deal with thephenomenon of cointegration in multivariate time series, we present a novelalgorithm denoted EC-VARMA-OGD. Our algorithms and regret analysis subsumesrecent related work while significantly expanding the domain of applicabilityof such methods. For all the methods we provide sub-linear regret bounds usingrelaxed assumptions. We note that the theoretical guarantees do not fullycapture the benefits of the nonstationary transformation, thus we provide adata-dependent analysis of the follow-the-leader algorithm for least squaresloss that provides insight into the success of using nonstationarytransformations. We support all of our results with experiments on simulatedand real data.
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