# Wave:Autocorrelation

Autocorrelation analysis for analyzing time series periodicity.

Autocorrelation refers to the degree of correlation of the same variables between two successive time intervals. It measures how the lagged version of the value of a variable is related to the original version of it in a time series.

In this analysis function, the input time series is repeatedly offset from the original version by a user-defined amount. For each offset (lag), the correlation coefficient between the lagged version and the original version is computed. The results are plotted in a diagram called autocorrelogram.

The peaks in the autocorrelogram show at which lag the autocorrelation value is high and give an indication about the periodicity of the time series. These peaks are estimated and drawn in the diagram. The distance between these peaks is used to estimate the periodicity of the time series according to Holzmann (2013)^{[1]}. Detailed analysis results are output to the log.

**Notes:**

- For best results, the input time series should not contain a trend
^{[2]}. - The input time series should be equidistant, as the offsets (lags) are based on numbers of time steps, regardless of the time between the individual time steps (you can use the analysis function TimestepAnalysis to analyze the time steps beforehand and the analysis function ChangeTimestep to create an equidistant time series).
- The autocorrelation coefficient becomes less accurate with increasing lag, because the number of available concurrent values for calculating the correlation coefficient becomes smaller.

This analysis function is based on the work of Rosskopf (2014)^{[3]}

## Literature

- ↑
**Holzmann, H.**(2013): Wasserwirtschaftliche Planungsmethoden – Zeitreihenanalyse, Institut für Wasserwirtschaft, Hydrologie und konstruktiven Wasserbau, Universität für Bodenkultur, Wien - ↑
**Nachtnebel, H.P.**(2003): Hydrologie – Studienblätter, Institut für Wasserwirtschaft, Hydrologie und konstruktiven Wasserbau, Universität für Bodenkultur, Wien - ↑
**Rosskopf, Tobias**(2014): Analyseverfahren hydrologischer Zeitreihen und deren Eignung für die Implementation in BlueM.Wave. Darmstadt, Technische Universität, Bachelor Thesis