Simple Example of Time Series Anomaly Detection Based on Postgresql

First, create a table containing time series data. For example, create a table named "time_series_data" with two fields: timestamp and value:

CREATE TABLE time_series_data (
    timestamp TIMESTAMP NOT NULL,
    value NUMERIC NOT NULL
);

Use window functions to calculate the moving average and moving standard deviation. For example, you can use the following query to calculate the moving average (moving_avg) and moving standard deviation (moving_stddev) for each data point over a window of 5 time units:

SELECT
    timestamp,
    value,
    AVG(value) OVER (ORDER BY timestamp ROWS BETWEEN 4 PRECEDING AND CURRENT ROW) AS moving_avg,
    STDDEV(value) OVER (ORDER BY timestamp ROWS BETWEEN 4 PRECEDING AND CURRENT ROW) AS moving_stddev
FROM
    time_series_data;

Calculate the Z-score for each data point to determine its distance from the moving average. You can use the following query to calculate the Z-score:

WITH moving_stats AS (
    SELECT
        timestamp,
        value,
        AVG(value) OVER (ORDER BY timestamp ROWS BETWEEN 4 PRECEDING AND CURRENT ROW) AS moving_avg,
        STDDEV(value) OVER (ORDER BY timestamp ROWS BETWEEN 4 PRECEDING AND CURRENT ROW) AS moving_stddev
    FROM
        time_series_data
)
SELECT
    timestamp,
    value,
    (value - moving_avg) / moving_stddev AS z_score
FROM
    moving_stats;

Identify data points as outliers based on the Z-score. For example, data points with a Z-score greater than 3 or less than -3 can be considered outliers. Use the following query to filter out the outlier data points:

WITH moving_stats AS (
    SELECT
        timestamp,
        value,
        AVG(value) OVER (ORDER BY timestamp ROWS BETWEEN 4 PRECEDING AND CURRENT ROW) AS moving_avg,
        STDDEV(value) OVER (ORDER BY timestamp ROWS BETWEEN 4 PRECEDING AND CURRENT ROW) AS moving_stddev
    FROM
        time_series_data
),
z_scores AS (
    SELECT
        timestamp,
        value,
        (value - moving_avg) / moving_stddev AS z_score
    FROM
        moving_stats
)
SELECT
    timestamp,
    value,
    z_score
FROM
    z_scores
WHERE
    z_score > 3 OR z_score < -3;

This method is based on statistical principles and assumes that the time series data follows a normal distribution. You can adjust the size of the moving window (e.g., change "ROWS BETWEEN 4 PRECEDING AND CURRENT ROW") and the threshold for outlier detection (e.g., change "z_score > 3 OR z_score < -3") according to your specific needs.