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Anomaly Detection in Seasonal Time Series

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Humberto Marchezi
Humberto Marchezi

Presentation on how to detect anomalies in seasonal time series by extracting and analysing the residual component from original signal.

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Anomaly Detection in Seasonal Time Series Humberto Cardoso Marchezi Manchester, UK 25 March 2019
Anomalies
Applicability ● Financial Fraud ● Manufacturing Inspection ● Network Intrusion Detection ● Web Service Disaster Discovery (DevOps) ● etc.
DevOps Use Case Machines are monitored through graphic analysis of CPU levels, memory consumption, etc.
DevOps Use Case However relying on human eyes to look at dashboards is not a scalable option. Automation is needed!
incidents Automated System Machine Collectors Incident Detection System metric data points Alarm Generator notifies DevOps Engineer
Case 1 machines reboots/year Machines that reboot too much are anomalies of interest. How to isolate them ?
machines reboots/year mean mean + 2 std mean - 2 std Case 1 Machines that reboot too much are anomalies of interest. How to isolate them ?
machines reboots/year threshold Case 1 Linear calculated threshold isolates anomalous data points
Case 2 How to isolate global and local anomalies in seasonal signal ?
Case 2 Linear threshold can identify global anomalies since they are outside of signal variation
????? Case 2 However there is no linear threshold to isolate the local anomalies. How to proceed ?
Seasonality and Frequency 1 data point every hour daily seasonality frequency = 24 Review signal characteristics: daily seasonality, one data point per hour, no visible trend
Additive vs Multiplicative Time Series International Airline Passengers per Month (multiplicative) Austria Industrial Production per Quarter (additive) Seasonality magnitude increases with trend Seasonality effect remains constant despite trend
● Multiplicative Model Seasonal Trend Decomposition = * * observed trend seasonal residual ● Additive Model = + + observed trend seasonal residual trend - long term signal behavior seasonal - identified repetitive behavior residual - all the rest that doesn’t fit the trend or seasonal
????? frequency = 24 model = additive Case 2 Recap problem: how to identify such local anomalies ?
Seasonal-Trend Decomposition original trend seasonal residual
original trend seasonal residual Seasonal-Trend Decomposition Residual is the component of interest for anomaly detection
Seasonal-Trend Decomposition original residual Global and local anomalies are mapped in the residual component
original residual Seasonal-Trend Decomposition Global and local anomalies are mapped in the residual component
residual Seasonal-Trend Decomposition Residual is free from trend and seasonal behavior
median median + 6 mad median - 6 mad Seasonal-Trend Decomposition residual Therefore anomalies can now be found with linear-based thresholds
median median + 6 mad median - 6 mad Seasonal-Trend Decomposition residual Therefore anomalies can now be found with linear-based thresholds
Residual Extraction Mapping the anomalies found in residual back to the original signal identifies all data points of interest
Residual Extraction Pros: ● Works well with seasonal time series - global and local anomalies ● Few parameters to optimize (compared to other models) ● Algorithm implementation is simple given statistics libraries as available Cons: ● Need to know how to adjust period parameter for each time series ● Need to know how to adjust anomaly factor so to avoid noisy results ● Works only for seasonal time series where residual is a normal distribution
References / Q&A Notebook Demo - https://github.com/hcmarchezi/jupyter_notebooks/blob/master/residual_extraction_demo_1.ipynb Anomaly Detection: A Tutorial - http://icdm2011.cs.ualberta.ca/downloads/ICDM2011_anomaly_detection_tutorial.pdf Twitter Anomaly Detection - https://github.com/twitter/AnomalyDetection Automatic Anomaly Detection in the Cloud Via Statistical Learning - https://arxiv.org/pdf/1704.07706.pdf Generalized ESD for Outliers - https://www.itl.nist.gov/div898/handbook/eda/section3/eda35h3.htm Real Time Anomaly Detection System for Time Series at Scale - http://proceedings.mlr.press/v71/toledano18a/toledano18a.pdf Time Series Dataset - https://datamarket.com/data/
The End

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