  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.
