Serial dependence, or autocorrelation, occurs when measurements are correlated because of sampling order or persistent system dynamics. Predictability between measurements signals nonindependence, even when observations are not strictly sequential. section 8.1.1
Repeated measurements understate uncertainty
Ten observations containing eight repeated 1.5 values plus 2.3 and 3.1 produce an estimated standard error of 0.16. Sampling one value per independent measurement instead gives 1.5, 2.3, and 3.1, with a standard error of 0.38. The repeated run makes the data appear more precise than they are. section 8.1.1
Practical safeguards include:
- Sample less frequently than the dependence-decay interval; this reduces correlated measurements but discards potentially useful data. section 8.1.1
- Model the serial dependence when discarding observations is too costly. section 8.1.1
