Discounted online Newton method for time-varying time series prediction

We develop an online convex optimization method for predicting time series based on streaming observations. We first approximate the evolution of time-varying autoregressive integrated moving average (ARIMA) processes and then propose a discounted online Newton method for estimating time-varying ARIMA time series. Under practical assumptions, we establish dynamic regret bounds that quantify the tracking performance of our algorithm. To verify the effectiveness and robustness of our method, we conduct experiments on prediction problems based on both artificial data and real-world COVID-19 data. To the best of our knowledge, we are the first to report a COVID-19 prediction that utilizes online learning.