Autocorrelation Function previously described is also called as Double Correlation Function. One more upgraded function is Triple Correlation Function. Autocorrelation Function and Triple Correlation Function can be defined as follow;
As you can see in formula (2), Autocorrelation Function relates to correlation between time series signal, x(t) , and time series signal delayed by τ , x(t+τ) Formula (3) clearly shows Triple Correlation Function. This relates to correlation between time series signal, x(t) time series signal delayed by τ , x(t+τ) and time series signal delayed by τj , x(t+τj). In other words, this shows correlation between three time series signals delayed by different times. Unlike Autocorrelation Function, this function enables you to know correlation between delayed signals, x(t+τj) and x(t+τj). in addition to correlation relative to original signal, so the result is expressed as 3-D graph.