Autoregressive Integrated Moving Average (ARIMA) Model for Anomaly Detection

1. Description of the model

The Autoregressive Integrated Moving Average (ARIMA) model is a popular time series forecasting model that has also been widely used for anomaly detection. It is a combination of three components:

Autoregressive (AR): This component models the relationship between an observation and a fixed number of lagged observations (i.e., its own past values). It helps capture the effect of history on the current observation.
Integrated (I): This component incorporates the concept of differencing to make the time series stationary. Differencing involves taking the difference between consecutive observations to remove trends or seasonal patterns.
Moving Average (MA): This component models the relationship between an observation and a residual error from a moving average of the lagged observations. It helps capture the effect of past forecast errors.

By combining these three components, ARIMA models can accurately capture both short-term dependencies through the autoregressive and moving average terms, as well as long-term trends and seasonality through differencing.

2. Pros and Cons of the model

Pros:

ARIMA models are generally easy to understand and interpret.
They can handle various types of time series data, including those with trend, seasonality, or both.
ARIMA models can capture both short-term and long-term dependencies in the data.
They can provide forecast values as well as anomaly scores based on the deviation from the expected values.

Cons:

ARIMA models may not perform well on data with irregular or non-linear patterns.
They are sensitive to outliers and require pre-processing or outlier detection techniques to handle anomalies in the training data.
ARIMA models require the data to be stationary, and determining the appropriate differencing order can be challenging.
These models assume that the future patterns will be the same as the past patterns, which may not always hold true.

3. Relevant Use Cases

Network Traffic Anomaly Detection: ARIMA models can be used to analyze network traffic data and detect anomalies such as sudden spikes or drops in traffic volume, which may indicate network attacks or equipment failures.
Financial Market Anomaly Detection: ARIMA models are commonly employed to identify abnormal price movements or trading patterns in financial markets, helping traders and investors in making informed decisions.
Power Grid Anomaly Detection: By analyzing power consumption data, ARIMA models can detect unusual usage patterns or deviations from expected power demands, indicating equipment malfunctions or electricity theft.

4. Resources for implementing the model

Python Statsmodels Library: Documentation
R Forecast package: Documentation and Time Series Analysis and Its Applications: With R Examples
Towards Data Science Article: Anomaly Detection with ARIMA in Python

5. Top 5 experts in ARIMA for Anomaly Detection

Rob J. Hyndman - GitHub
Jason Brownlee - GitHub
Sebastian Raschka - GitHub
Ethan Rosenthal - GitHub
Paulo Vasconcellos - GitHub

Relevant Internal Links

Data Type : TimeSeriesData
Problem type : AnomalyDetection