pg_stl

Overview

ACF, PACF, STL decomposition, and Holt-Winters forecasting.

Version

Build

You can build the RPM / DEB packages for pg_stl using pig build:

pig build pkg pg_stl         # build RPM / DEB packages

Install

You can install pg_stl directly. First, make sure the PGDG and PIGSTY repositories are added and enabled:

pig repo add pgsql -u          # Add repo and update cache

Install the extension using pig or apt/yum/dnf:

• Install
• pig
• dnf
• apt

pig install pg_stl;          # Install for current active PG version

pig ext install -y pg_stl -v 18  # PG 18
pig ext install -y pg_stl -v 17  # PG 17
pig ext install -y pg_stl -v 16  # PG 16

dnf install -y pg_stl_18       # PG 18
dnf install -y pg_stl_17       # PG 17
dnf install -y pg_stl_16       # PG 16

apt install -y postgresql-18-pg-stl   # PG 18
apt install -y postgresql-17-pg-stl   # PG 17
apt install -y postgresql-16-pg-stl   # PG 16

Create Extension:

CREATE EXTENSION pg_stl;

Usage

Sources: pg_ts_analysis README, SQL definitions, control file.

pg_stl provides time-series analysis functions for PostgreSQL: autocorrelation, partial autocorrelation, STL decomposition, and Holt-Winters forecasting. The upstream README and SQL definitions target PostgreSQL 16+.

Autocorrelation

acf_array(data double precision[], lags integer) returns autocorrelation values for lags 1..lags:

CREATE EXTENSION pg_stl;

SELECT acf_array(
  array_agg(revenue ORDER BY date)::double precision[],
  28
)
FROM daily_sales;

The README describes using peaks at lags such as 7, 14, and 21 as a signal for weekly seasonality. The function returns NULL when the series is too short, lags < 1, or lags >= n.

Partial Autocorrelation

pacf_array(data double precision[], lags integer) returns partial autocorrelation values using the Durbin-Levinson recursion:

WITH series AS (
  SELECT array_agg(value ORDER BY ts)::double precision[] AS values
  FROM measurements
)
SELECT
  unnest(acf_array(values, 20)) AS acf,
  unnest(pacf_array(values, 20)) AS pacf
FROM series;

Use PACF when you want the direct lag relationship after accounting for shorter lags.

STL Decomposition

stl_decompose decomposes a series into trend, seasonal, and residual arrays:

WITH data AS (
  SELECT array_agg(revenue ORDER BY month)::double precision[] AS values
  FROM monthly_revenue
),
decomposed AS (
  SELECT (stl_decompose(values, 12)).*
  FROM data
)
SELECT
  unnest(trend) AS trend,
  unnest(seasonal) AS seasonal,
  unnest(residual) AS residual
FROM decomposed;

Signature from the SQL definition:

stl_decompose(
  y double precision[],
  period integer,
  seasonal integer DEFAULT 7,
  robust boolean DEFAULT true,
  trend integer DEFAULT 0,
  low_pass integer DEFAULT 0,
  inner_iter integer DEFAULT 2,
  outer_iter integer DEFAULT 0
) RETURNS stl_result

Use the convenience functions when only one component is needed:

SELECT stl_trend(values, 12) FROM series;
SELECT stl_seasonal(values, 12) FROM series;
SELECT stl_residual(values, 12) FROM series;

Ordered Collection Helper

The SQL file also defines stl_collect_ordered(tbl regclass, val text, ord text) to collect a column into an ordered double precision[]:

SELECT stl_decompose(
  stl_collect_ordered('monthly_revenue'::regclass, 'revenue', 'month'),
  12
);

Holt-Winters Forecasting

holt_winters_predict(seasonal_type text, period_length int, start_data_array real[]) forecasts one seasonal cycle ahead. seasonal_type is 'mult' for multiplicative seasonality or 'add' for additive seasonality:

SELECT *
FROM holt_winters_predict(
  'mult',
  4,
  (SELECT array_agg(revenue ORDER BY date)::real[] FROM sales)
);

The SQL implementation chooses smoothing coefficients automatically: first by 500 random initializations, then by refinement in 0.001 steps to minimize squared error. The helper holt_winters_mse(...) is present as the error-calculation routine used by the predictor.

Caveats

• stl_decompose expects a double precision[] with no NULL values.
• The README states the series length must be at least 2 * period.
• seasonal must be an odd integer greater than or equal to 3.
• Holt-Winters expects a real[] input and supports only 'mult' and 'add' seasonal types.