In statistics and signal processing, random variables in a time series have serial dependence if the value at some time t in the series is statistically dependent on the value at another time s. A series is serially independent if there is no dependence between any pair.
Similarly, a time series has serial correlation if the condition holds that some pair of values are correlated, rather than the condition of statistical dependence: see autocorrelation.
If a time series {Xt} is stationary, then statistical dependence between the pair (Xt , Xs) would imply that there is statistical dependence between all pairs of values at the same lag s−t.