Autocorrelation results
Results reflect the selected preprocessing, lag, confidence, and estimator settings.
White-noise tests
Stationarity support
| Index | Current value | Lagged value | Difference |
|---|
| Lag | ACF | Covariance | Pair count | Lower bound | Upper bound | Significant |
|---|
The sample autocorrelation at lag k compares each observation with an earlier observation. It measures repeated linear structure across the series. The result always lies near minus one and one.
Approximate pointwise confidence bounds use a normal critical value. Bartlett-style bounds widen using preceding autocorrelations. These bounds are exploratory, not simultaneous inference across every lag.
- Enter values or upload a CSV file.
- Select the primary numeric column when needed.
- Configure missing values, transformations, and differencing.
- Choose lag, confidence, estimator, and plotting options.
- Calculate, inspect significant lags, and export results.
| Month | Demand | Possible pattern |
|---|---|---|
| 1 | 120 | Starting level |
| 2 | 128 | Short-term persistence |
| 3 | 135 | Rising movement |
| 12 | 122 | Potential seasonal return |
| 13 | 127 | Lag-twelve comparison |
Positive spikes indicate observations move together across the selected lag. Negative spikes indicate alternating movement between paired observations. Small spikes indicate limited linear dependence at that lag.
Slow decay can indicate trend, persistence, or non-stationarity. Repeated peaks at seasonal multiples can indicate recurring structure. Rapid decay often reflects a shorter-memory time-series process.
ACF supports model identification but does not choose models alone. PACF measures direct lag effects after shorter lags. Stationarity checks and domain knowledge should guide final decisions.
What does autocorrelation measure?
It measures linear similarity between a series and lagged copies. Values near one show positive repetition. Values near minus one show alternating behavior.
Why does lag zero equal one?
Lag zero compares every observation with itself. Both sequences are identical. Their normalized correlation therefore equals exactly one.
What is a significant ACF spike?
It crosses the selected approximate confidence boundary. The spike deserves investigation. It does not establish a complete time-series model.
How should maximum lag be selected?
Use enough lags to expose meaningful cycles. Avoid using nearly the entire sample. Later lags contain fewer reliable observation pairs.
When should I difference the series?
Differencing can reduce trends and persistent level shifts. Consider it when ACF values decay slowly. Verify that differencing does not remove meaningful structure.
What is seasonal differencing?
It subtracts values separated by a seasonal period. Monthly data often uses period twelve. Weekly data may use period fifty-two.
How do ACF and PACF differ?
ACF includes direct and indirect lag relationships. PACF controls for shorter intermediate lags. Both plots support ARIMA order exploration.
What do Ljung–Box results mean?
The test evaluates several autocorrelations jointly. A small p-value rejects white-noise behavior. The chosen test lag affects the conclusion.
Can irregularly spaced data use ACF?
Standard ACF assumes regular observation spacing. Irregular timing can distort lag meaning. Resample or interpolate carefully before interpretation.
Can missing values change results?
Yes, deletion and imputation alter observation pairs. Different methods may produce different spikes. Report the selected missing-value method clearly.
Does autocorrelation prove causation?
No, it only measures repeated linear association. Trends can create misleading autocorrelation. External causes require separate evidence and analysis.