# Cross correlation

Cross-correlation (Davis 1986) is carried out on two column(s) of evenly sampled temporal/stratigraphic data. The *x* axis shows the displacement of the second column with respect to the first, the *y* axis the correlation between the two time series for a given displacement. The "p values" option will draw the significance of the correlation, after Davis (1986).

For two time series **x** and **y**, the cross-correlation value at each lag time *m* is computed.

For positive lags, **x** is compared with a **y** that has been delayed by *m* samples. A high correlation value at positive lags thus means that features in **y** are leading, while **x** lags behind. For negative lags, features in **x** are leading. A reminder of this is given by the program.

The *p* value for a given *m* is given by a *t* test with *n*-2 degrees of freedom, with *n* the number of samples that overlap.

It is important to note that this test concerns *one particular m*. Plotting *p* as a function of all *m* raises the issue of multiple testing – *p* values smaller than 0.05 are expected for 5% of lag times even for completely random (uncorrelated) data sets.

Missing data supported.

#### Reference

Davis, J.C. 1986. Statistics and Data Analysis in Geology. John Wiley & Sons.