Incremental-decremental rolling window double exponential smoothing

Abstract

By modeling double exponential smoothing as a weighted directed acyclic graph, we design an implementation of rolling window double exponential smoothing which is incremental-decremental in the sense that points can be added to and removed from the window with overhead and computation independent of the window size. This has applications to real-time streaming analytics systems having certain universality and flexibility requirements.

Keywords:

• Exponential smoothing
• Holt–Winters
• Incremental Decremental algorithm
• Rolling window method

Acknowledgments

It is a pleasure to thank engineering and management at SignalFx for their encouragement and support during the preparation of this paper.

Notes

1 This project arose from the author’s work on a commercial software product that facilitates analytics on time series of metrics produced by computing infrastructure (e.g., CPU utilization) with the goal of monitoring the health of that infrastructure. The work described here has been incorporated into that product (Ross 2017).

2 In our particular software implementation, for example, we choose the window size so that both $${(1-\alpha )}^n$$ and $${(1-\beta )}^n$$ are less than some small positive number.