Autocorrelation
ACF, PACF, and Ljung–Box on one numeric series.
When to use it
Use autocorrelation when you want to see which lags still line up with the series, before you pick an ARIMA order. Stationarity of the same series is stationarity tests.
Assumptions
The target is numeric, with at least eight non-missing values. Maximum lags starts at 20 and is capped at N − 2. ACF uses the FFT estimator. PACF uses Yule–Walker. Ljung–Box is printed at lags 10 and 20 when those lags fit under the cap.
Running it in Tensr
Options
Prop
Type
Reading the output
The noise column on those 48 months, drawn as independent N(50, 4) values. Lag structure here is leftover chance, not the sales season.
| Lag | ACF | Lower 95% | Upper 95% | Significant |
|---|---|---|---|---|
| 0 | 1 | — | — | — |
| 1 | -0.147 | -0.283 | 0.283 | No |
| 2 | -0.04 | -0.283 | 0.283 | No |
| 3 | -0.112 | -0.283 | 0.283 | No |
| 4 | -0.016 | -0.283 | 0.283 | No |
| 5 | 0.039 | -0.283 | 0.283 | No |
| 6 | 0.125 | -0.283 | 0.283 | No |
| 7 | 0.02 | -0.283 | 0.283 | No |
| Lag | PACF | Lower 95% | Upper 95% | Significant |
|---|---|---|---|---|
| 0 | 1 | — | — | — |
| 1 | -0.147 | -0.283 | 0.283 | No |
| 2 | -0.063 | -0.283 | 0.283 | No |
| 3 | -0.13 | -0.283 | 0.283 | No |
| 4 | -0.06 | -0.283 | 0.283 | No |
| 5 | 0.012 | -0.283 | 0.283 | No |
| 6 | 0.119 | -0.283 | 0.283 | No |
| 7 | 0.06 | -0.283 | 0.283 | No |
ACF and PACF on independent draws should sit inside the 95% bands at most lags. Ljung–Box at lag 10: Q = 3.697, p = .960.
Reporting (APA 7)
ACF and PACF of the noise series, N = 48, max lags = 20. Ljung–Box p = .960 at lag 10.
Coming from SPSS
SPSS is Analyze → Forecasting → Autocorrelations. Tensr’s item is Time series → Decomposition → Autocorrelation. The path string stored for this item says Time series → Diagnostics → ACF / PACF. The item itself sits under Decomposition with STL.
Related
Stationarity tests are the other diagnostic. ARIMA / SARIMA is the forecast those plots are meant to inform.