Statistical Methods
Compute and interpret a sample autocorrelation at a chosen lag
Start with the time grid
Choose a lag that has a clear meaning, such as one weekly reporting cycle. Verify the spacing of observations. Removing a missing week and treating the remaining values as adjacent changes the estimand. Keep the original ordering and resolve gaps explicitly.
Center once
In the conventional sample autocorrelation, subtract the full-series mean from every value. Sum products of deviations at the chosen lag, and divide by the sum of squared deviations for all observations. Computing a Pearson correlation between two shortened vectors uses different means and a different denominator.
Hypothetical calculation
For the ordered series 1, 2, 3, 4, the mean is 2.5 and the squared deviations sum to 5. At lag one, the three paired products are 0.75, −0.25 and 0.75. The sample autocorrelation is 1.25/5 or 0.25. Correlating the vectors (1,2,3) and (2,3,4) would give 1. Both numbers have a mathematical meaning, so record the convention used.
Inspect the time plot for a trend or structural change before attributing the result to short-memory dependence. Longer lags have fewer contributing pairs. A flat series has zero variance and an undefined autocorrelation. For a descriptive screen, report the lag, number of pairs and estimate without assigning an automatic significance label.
Method checked 9 November 2026. NIST/SEMATECH Engineering Statistics Handbook, 1.3.3.1. Autocorrelation Plot.