Anomaly Detection for Time Series

The local beach is not far from where I live, so sometimes I go there to enjoy my solitude. I watch the ocean waves come and go, leaving a belt of wet sand. I watch my footprints along the wet sand appear and disappear. One day I had an aha moment. These footprints are like the data points in a time series, and the belt of the wet sand is the acceptable range by a time series model. There are a few footprints outside the belt called anomalies or outliers. When the belt covers the normal footprints, none of them is anomalous. But when the belt moves, some footprints are exposed outside the belt and become anomalies.

Figure (I): The same data with two different models

This ocean stroll reminds me of the challenge of building a time series model to identify anomalies accurately. The challenges are: (i) considering anomalies as normal footprints, and (ii) considering normal footprints as anomalies. Figure (I) shows one model may consider data as anomalous but another model may not. How do we tackle these challenges? I know the following two steps are essential: (1) understanding the data patterns and source of noises, and then (2) choosing suitable techniques.

Data patterns are patterns that have happened in the past and are likely to repeat in the…