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Rolling standard deviation

documentation/cookbook/sql/finance/rolling-stddev.md

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Calculate rolling standard deviation to measure price volatility over time.

Problem

You want to calculate rolling standard deviation.

Solution

Use the mathematical identity: σ = √(E[X²] - E[X]²)

Compute both AVG(price) and AVG(price * price) as window functions, then derive the standard deviation:

questdb-sql
WITH stats AS (
  SELECT
    timestamp,
    symbol,
    price,
    AVG(price) OVER (PARTITION BY symbol ORDER BY timestamp) AS rolling_avg,
    AVG(price * price) OVER (PARTITION BY symbol ORDER BY timestamp) AS rolling_avg_sq
  FROM fx_trades
  WHERE timestamp IN '$yesterday' AND symbol = 'EURUSD'
)
SELECT
  timestamp,
  symbol,
  price,
  rolling_avg,
  SQRT(rolling_avg_sq - rolling_avg * rolling_avg) AS rolling_stddev
FROM stats
LIMIT 10;

How it works

The mathematical relationship used here is:

Variance(X) = E[X²] - (E[X])²
StdDev(X) = √(E[X²] - (E[X])²)

Where:

  • E[X] is the average (SMA) of prices
  • E[X²] is the average of squared prices
  • √ is the square root function

This query calculates an expanding standard deviation from the beginning of the period to the current row. For a fixed rolling window, add a frame clause to both window functions using ROWS (fixed number of rows) or RANGE (time-based window).

:::info Related documentation