Editing Autocorrelation (section)

== Serial dependence ==
'''Serial dependence''' is closely linked to the notion of autocorrelation, but represents a distinct concept (see [[Correlation and dependence]]). In particular, it is possible to have serial dependence but no (linear) correlation. In some fields however, the two terms are used as synonyms.

A  [[time series]] of a [[random variable]] has serial dependence if the value at some time <math>t</math> in the series is [[Statistical independence|statistically dependent]] on the value at another time <math>s</math>. A series is serially independent if there is no dependence between any pair.

If a time series <math>\left\{ X_t \right\}</math> is [[Stationary process|stationary]], then statistical dependence between the pair <math>(X_t,X_s)</math> would imply that there is statistical dependence between all pairs of values at the same lag <math>\tau=s-t</math>.