**How to do anomaly detection in time series? What different algorithms are commonly used? How do they work, and what are the advantages and disadvantages of each method? Be able to choose the right method for your application. The most common libraries for Python and R are listed with the algorithms they implement. **

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## What is anomaly detection for time series?

Anomaly detection in time series data involves finding patterns or behaviours different from how the system being watched is supposed to act.

Time series data is a list of data points collected at regular or irregular intervals. Anomalies in time series data could mean the system being watched is broken or acting strangely.

Here are some standard methods used for anomaly detection in time series data:

**Statistical methods**involve looking for outliers by analysing the time series’ mean, variance, or distribution. One commonly used statistical method is the Z-score, which measures the distance between a data point and the mean in terms of standard deviations.**Machine learning methods**involve training a machine learning model to detect anomalies in time series data. Popular machine learning algorithms for anomaly detection include support vector machines (SVMs), decision trees, and neural networks.**Signal processing methods**involve analysing the signals generated by the system being monitored and detecting anomalies by identifying changes in the signal patterns. Examples of signal processing methods include Fourier analysis and wavelet analysis.**Hybrid methods**combine multiple techniques to improve anomaly detection accuracy. For example, a hybrid method may use statistical methods to detect anomalies in the time domain and machine learning techniques to detect abnormalities in the frequency domain.

It’s essential to remember that the suitable method for finding anomalies depends on the time series data being analysed and the goals of the analysis.

## Top 8 time series anomaly detection algorithms

Many time series anomaly detection algorithms can detect unusual patterns or behaviours in time series data. Here are the most commonly used ones:

### 1. Statistical Process Control (SPC)

This method uses statistical tools like control charts to find patterns that don’t fit with how the system is supposed to work. For example, a control chart plots data over time and uses statistical methods to identify when a process is out of control.

**Advantages**

- SPC is a method that has been used for a long time in quality management and process control.
- It is easy to use and understand, so experts and people who aren’t experts in statistical analysis can use it.
- It can be used to find a wide range of unusual things in time series data, such as shifts, trends, and cycles.

**Disadvantages**

- For SPC, you have to choose an effective type of control chart, which can be challenging and takes some domain knowledge.
- It assumes that the process under investigation is stable and stays the same over time, which may not always be the case.
- It might not be suitable for finding anomalies in time series data that are complicated and hard to spot.

**Applications**

- SPC is used in the manufacturing and process industries to track and control how things are made.
- It can be used in healthcare to monitor patients’ vital signs and detect abnormal values.
- It can be used in finance to find stock price changes or changes in trading volume that don’t make sense.

Statistical Process Control (SPC) is used in healthcare to monitor patients’ vital signs

### 2. Seasonal decomposition of time series

This method breaks down a time series into seasonal, trend, and residual parts. The residual component can be analysed to detect anomalies.

**Advantages**

- Seasonal decomposition breaks down time series data into its basic parts, making spotting oddities in the residual component easier.
- It is suitable for detecting seasonal and periodic anomalies in the time series data.
- It can be used with various statistical methods for anomaly detection.

**Disadvantages**

- Seasonal decomposition assumes that the seasonal and trend parts of the time series data stay the same over time, which isn’t always the case.
- It requires selecting appropriate decomposition parameters, which may require some expertise.
- It may not be suitable for detecting non-seasonal anomalies in the time series data.

**Applications**

- Seasonal decomposition can be used to find seasonal patterns in temperature, rain, and other weather-related variables in environmental monitoring.
- It can be used in marketing to look at how sales change with the seasons and find strange sales trends.
- It can be used in finance to find seasonal patterns in the prices of stocks and the number of trades that happen.

### 3. Moving Average

This simple method smoothes the time series data by taking the average of a fixed window of data points. When a data point falls outside a specific range of the moving average, this can be used to find anomalies.

**Advantages**

- The moving average is a simple method that is easy to implement and interpret.
- It can be used to smooth the time series data, making it easier to spot outliers.
- It is suitable for detecting short-term fluctuations in the time series data.

**Disadvantages**

- The moving average assumes that the time series data is stationary and does not change over time, which may not always be accurate.
- It might not be suitable for finding long-term trends or seasonal patterns in time series data.
- It might not be suitable for finding anomalies in time series data that are complicated and hard to spot.

**Applications**

- A moving average can be used to find short-term traffic changes and patterns of congestion when monitoring traffic.
- In finance, it can be used to find short-term changes in stock prices and the number of trades.
- It can be used in energy management to detect short-term fluctuations in energy consumption.

### 4. Exponential smoothing

This method uses a weighted average to smooth the time series data, giving more weight to recent data points. Anomalies can be detected when the data point deviates significantly from the smoothed value.

**Advantages**

- Exponential smoothing is a simple method that is easy to implement and interpret.
- It can smooth the time series data and find outliers based on how much the smoothed value deviates from the average.
- It is suitable for detecting short-term fluctuations and trends in the time series data.

**Disadvantages**

- Exponential smoothing assumes that the time series data doesn’t change over time and stays the same, which isn’t always true.
- It might not be suitable for finding anomalies in time series data that are complicated and hard to spot.
- It may require some expertise in selecting appropriate smoothing parameters.

**Applications**

- Exponential smoothing can be used in energy management to detect short-term fluctuations in energy consumption.
- In finance, it can be used to find short-term changes in stock prices and the number of trades.
- Demand forecasting can predict short-term demand patterns and spot unusual spikes in demand.

### 5. Autoregressive Integrated Moving Average (ARIMA)

This is a popular method for time series forecasting that can also be used for anomaly detection. It models the time series as a combination of autoregressive, moving average, and differencing components and can be used to detect unusual patterns in the residuals.

**Advantages**

- ARIMA is a well-known method that can be used to model a wide range of time series data, even data that doesn’t stay the same over time.
- It can be used to find a wide range of strange things in time series data, such as shifts, trends, and cycles.
- It can generate forecasts for future periods based on past data.

**Disadvantages**

- For ARIMA, choosing the correct model parameters, such as the order of differencing and the number of autoregressive and moving average terms, takes some knowledge.
- It might not be suitable for finding long-term trends or seasonal patterns in time series data.
- It might not be good for finding anomalies in time series data that are complicated and hard to spot.

**Applications**

- ARIMA can be used in demand forecasting to predict future demand patterns and detect unusual demand spikes.
- It can be used in finance to determine how much a stock will go up or down in the future and spot unusual trading volumes.
- It can be used in health care to predict how a patient’s vital signs will change and find strange patterns.

### 6. LSTM neural networks

This is a deep learning algorithm that is often used to predict sequences and can also be used to find out when something isn’t right. For example, LSTM models can find complex temporal dependencies in time series data and find unusual patterns based on the difference between the predicted and actual values.

**Advantages**

- LSTM neural networks are very good at capturing and modelling time series data with complex temporal dependencies.
- They can process input sequences of variable length and can handle missing data.
- They can generate accurate predictions for future periods based on past data.

**Disadvantages**

- LSTM neural networks can be computationally intensive and require significant computing resources.
- They may require a large amount of training data to achieve high accuracy.
- They can be sensitive to the hyperparameters you choose, and you may need some knowledge to tune them well.

**Applications**

- LSTM neural networks can find outliers in a wide range of time series data, such as stock prices, sensor data, and healthcare data.
- They can be used for demand forecasting in industries such as retail and manufacturing.
- They can be used to predict how sales will go or find strange patterns in sales data.

### 7. One-class SVM

This machine learning algorithm can detect anomalies in time series data. It learns the regular pattern of the time series data and detects anomalies based on the deviation from this typical pattern.

**Advantages**

- One-class SVM works well for finding outliers in high-dimensional data, which traditional statistical methods may have trouble with.
- It is easy to set up and has fewer parameters to tune than other machine learning algorithms.
- It can handle imbalanced datasets with fewer anomalous observations than regular observations.

**Disadvantages**

- One-class SVM may not be as good at finding outliers in complex data or doesn’t follow a straight line.
- It can be sensitive to the choice of kernel function and its associated parameters.
- It may require a large amount of training data to achieve high accuracy.

**Applications**

- In cybersecurity, one-class SVM can be used for intrusion detection to find strange network traffic patterns.
- It can be used in finance to find suspicious transactions or ways credit cards are used.
- It can be used in factories to monitor how machines work and look for strange patterns in sensor data.

### 8. Bayesian Online Changepoint Detection (BOCD)

The Bayesian Online Changepoint Detection (BOCD) algorithm is a method for detecting changes or anomalies in time series data. It is an online algorithm that can detect real-time changes as new data points are added to the time series.

At a high level, the BOCD algorithm works by modelling the underlying probability distribution of the time series using Bayesian statistics. The algorithm assumes that the time series is generated by a sequence of latent variables, each with its probability distribution. A change point is then defined as a time step where the distribution of the latent variables changes.

**Advantages**

- BOCD is an online algorithm that can detect real-time changes as new data points are added to the time series. This makes it particularly useful for applications where real-time detection is critical.
- BOCD uses Bayesian statistics to model the underlying probability distribution of the time series, making it robust to noise and able to handle complex data distributions.
- BOCD can detect multiple changes in the time series, which can be useful in identifying complex anomalies that may involve multiple events or sources.

**Disadvantages**

- BOCD requires tuning of hyperparameters such as the prior distribution and the penalty parameter, which can be time-consuming and require some expertise.
- BOCD can be sensitive to the choice of hyperparameters, impacting its performance and accuracy.
- BOCD may not be well-suited for detecting anomalies in short time series data, as it may require more data points to identify statistically significant changes.

**Applications**

- BOCD can detect changes or anomalies in a wide range of time series data, including stock prices, sensor data, and healthcare data.
- It can monitor industrial processes or detect anomalous behaviour in online applications such as cybersecurity.
- BOCD can be useful in anomaly detection applications where the data distribution is complex or difficult to model using traditional statistical methods.

## Best time series anomaly detection libraries in Python & R

Python & R have many libraries and packages for time series anomaly detection. Here are some popular libraries and packages for time series anomaly detection:

- Statsmodels: This is a library for statistical modelling and time series analysis. It includes a range of statistical methods for time series anomaly detection, including ARIMA, exponential smoothing, and seasonal decomposition of time series.
- Scikit-learn: This is a popular machine-learning library in Python. It includes a range of machine learning algorithms that can be used for time series anomaly detection, including one-class SVM and Isolation Forest.
- PyOD: This is a Python library for outlier detection that includes a range of algorithms that can be used for time series anomaly detection, including Isolation Forest, Local Outlier Factor, and k-Nearest Neighbors.
- Prophet: This is a time series forecasting library developed by Facebook. It includes a range of statistical methods for time series analysis, including trend detection, seasonality detection, and changepoint detection, which can be used for anomaly detection.
- Kats: Facebook developed a library that includes a variety of time series analysis and forecasting techniques, such as ARIMA, Prophet, and LSTM neural networks. It also has a range of methods for anomaly detection in time series data.
- AnomalyDetection: This library for R that Twitter developed includes a variety of statistical and machine learning techniques for anomaly detection in time series data, including Holt-Winters, Twitter’s anomaly detection algorithm, and Random Cut Forest.

The choice of library or package depends on the specific needs of the analysis, such as the type of time series data being analysed, the desired level of accuracy, and the particular anomaly detection algorithm needed.

## Anomaly detection time series conclusion

Time series anomaly detection is an important problem in many fields, such as finance, healthcare, and industrial monitoring. Many algorithms and methods can be used to find outliers in time series data. However, each has its pros and cons.

Some popular algorithms discussed include one-class SVM, LSTM neural networks, and the Bayesian Online Changepoint Detection (BOCD) algorithm. One-class SVM is effective for detecting anomalies in high-dimensional data, LSTM neural networks are highly effective at capturing and modelling complex temporal dependencies in time series data, and BOCD is an online algorithm that can detect changes in real-time as new data points are added to the time series.

Python libraries such as scikit-learn and TensorFlow implement these algorithms, making them easy to use and customise for specific applications. However, it is crucial to carefully evaluate the strengths and limitations of each algorithm and select the most appropriate approach in the particular use case at hand.

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