Change over time

Partial autocorrelation plot (PACF)

Shows correlation with each lag after accounting for intermediate lags.

Plot
Serial dependence
Model diagnostics

What it answers

Which lag relationships remain after shorter lags are accounted for?

Shape: Partial-correlation stems by lag
What it shows: Direct lag association conditional on intervening lags.

Example

The question

Which past weeks directly predict this week’s sales?

Partial autocorrelation of weekly sales by lag (PACF)

Once shorter lags are allowed for, only lag 1 (0.72) and lag 4 (0.36) stand clear of the noise band: last week and four weeks ago carry direct information.

Illustrative data. It belongs to no company.

When to use it

Use it when

Time-series model exploration.

Avoid it when

Treating stems as standalone causal effects.

How to read it

Read partial-correlation stems by lag and the estimator definition.

Note

Estimation methods vary across implementations.

The data you need

Layout: Long table
Fields: Time: date/datetime or ordered number; Value: number
One row is: One observation at a time or ordered position. What is the grain?
Rules: Parse dates consistently and sort ascending. Resolve duplicate timestamps by a declared rule. Missing values are not automatically zero.
Optional: Optional Series. Use regular spacing for methods requiring it.
Preparation: Prepare a regularly spaced series and calculate PACF using a declared estimator and maximum lag.
Units: Partial correlation is unitless; each lag uses the series's sampling interval.

A long table: one row per observation, few columns. New data adds rows.

Worked example

A supplied PACF has lag 1=0.7, lag 2=0.05. The lag 2 partial relationship is weak after accounting for lag 1.

Time	Value
2026-01-01	30
2026-02-01	34
2026-03-01	38

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