Autoregressive integrated moving average (ARIMA) is one of the most popular linear models for time series forecasting due to its nice statistical properties and great flexibility. However, its parameters are estimated in a batch manner and its noise terms are often assumed to be strictly bounded, which restricts its applications and makes it inefficient for handling large-scale real data. In this paper, we propose online learning algorithms for estimating ARIMA models under relaxed assumptions on the noise terms, which is suitable to a wider range of applications and enjoys high computational efficiency. The idea of our ARIMA method is to reformulate the ARIMA model into a task of full information online optimization (without random noise terms). As a consequence, we can online estimation of the parameters in an efficient and scalable way. Furthermore, we analyze regret bounds of the proposed algorithms, which guarantee that our online ARIMA model is provably as good as the best ARIMA model in hindsight. Finally, our encouraging experimental results further validate the effectiveness and robustness of our method.
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