Cross-Correlation
The cross-correlation method measures the similarity of two equally spaced time series with time shift. For this purpose, the correlation coefficients are calculated for different shifts of the two time series. A special case is the determination of the correlation of a time series to itself under time shift, the autocorrelation.
The time points of the resulting time series result from the shift of one time series against the fixed time series.
The data values of the new time series are the correlation coefficients from the fixed and the shifted time series and thus lie between -1 and 1.
The following figure illustrates schematically how the cross-correlation is determined.
Applying the Method
To start the method, select Methods → Analyze Time Series → Cross-correlation from the menu bar or the context menu of the time series in the Project Explorer (see figure below).
In the window that opens (see figure below), select the Fixed Time Series and the Shifted Time Series. A multiple selection is not possible.
Specify the Minimum Overlap by the Percentage of samples in the shorter time series or the Number of samples (data points).
Two abstract time series with the names CC_positive_shift and CC_negative_shift are generated (see following figure).
Autocorrelation
Autocorrelation is the special form of cross-correlation in which the Fixed and the Shifted Time Series are identical (see following figure).
The following plot of the autocorrelation of power demand clearly shows the daily and weekly rhythm of the time series.
