Change over time

Autocorrelation plot (ACF)

Shows correlation between a series and lagged versions of itself.

Plot
Serial dependence
Model diagnostics

What it answers

How strongly does a series resemble its earlier values?

Shape: Correlation stems by lag
What it shows: Serial dependence and recurring lag structure.

Example

The question

Do weekly sales echo earlier weeks, for example a monthly cycle?

Autocorrelation of weekly sales by lag (ACF)

Bars show how strongly sales correlate with sales a given number of weeks earlier; dashed lines mark the 95% noise band. Lags 1 to 5 and the peaks at weeks 4 and 8 stand out, hinting at a four-week cycle.

Illustrative data. It belongs to no company.

When to use it

Use it when

Time-series diagnostics with appropriate spacing.

Avoid it when

Irregular intervals treated as equal lags or trend ignored.

How to read it

Read correlation at each lag and any stated reference bounds.

Note

Use consistent ordering, spacing and missing-period rules.

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: Order a regularly spaced series, apply any justified detrending and calculate ACF with a stated estimator.
Units: Correlation is unitless. Lag units follow sample spacing, such as days or months.

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

Worked example

A supplied ACF has lag 1=0.7, lag 2=0.2. Adjacent observations show stronger linear dependence than observations two steps apart.

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

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