Time Series Using Exponential Smoothing Cells

Time series analysis is used to understand and predict dynamic processes, including evolving demands in business, weather, markets, and biological rhythms. Exponential smoothing is used in all these domains to obtain simple interpretable models of time series and to forecast future values. Despite its popularity, exponential smoothing fails dramatically in the presence of outliers, large amounts of noise, or when the underlying time series changes. We propose a flexible model for time series analysis, using exponential smoothing cells for overlapping time windows. The approach can detect and remove outliers, denoise data, fill in missing observations, and provide meaningful forecasts in challenging situations. In contrast to classic exponential smoothing, which solves a nonconvex optimization problem over the smoothing parameters and initial state, the proposed approach requires solving a single structured convex optimization problem. Recent developments in efficient convex optimization of large-scale dynamic models make the approach tractable. We illustrate new capabilities using synthetic examples, and then use the approach to analyze and forecast noisy real-world time series. Code for the approach and experiments is publicly available.