Statistics, experimentation, causal reasoning · insight-1026

Check residual autocorrelation in an interrupted time series and widen the intervals if it is there

Situation
A weekly interrupted time series after a schedule change gives a narrow, significant level shift from an ordinary least squares fit.
Action
Plot and test the model residuals for autocorrelation. If present, use standard errors robust to it (Newey-West type) or model the serial correlation explicitly, and re-read the level change against the wider interval.
Reason
Least squares assumes independent errors; positive serial correlation shrinks apparent uncertainty and inflates significance.
Boundary
Single-series before-and-after evaluations with weekly or daily data.

Symptom or risk

Successive weeks are correlated, so ordinary standard errors are too small and a modest shift looks decisive.

Residuals that look like white noise after seasonal and trend terms.

Wider intervals make weak effects non-significant; that is the honest answer.

Fixing autocorrelation by adding many lags that absorb the intervention effect.

The ITS tutorial advises checking residual autocorrelation, and notes that seasonality and events coinciding with the intervention can bias the estimates.
Interrupted time series regression for the evaluation of public health interventions: a tutorial