Multivariate Auto- and Cross-correlation Analysis

Frequently, concentration variations in environmental matrices not only concern themselves with one-dimensional cases, e.g. the time series of one parameter as discussed before, but also with many parameters which change simultaneously. In environmental analysis in particular, such time or local changes of environmental contaminants are very relevant [GEISS and EINAX, 1992], Multivariate time series models are available, 

A relevant question is the plotting of multivariate auto- or cross-correlation functions to determine multivariate relationship to lag. 

In environmental analysis there are two problems which need to be solved  

For this purpose the well-known univariate correlation analysis was changed to the more general multivariate case [GEISS and EINAX, 1991 1996]. Multivariate correlation analysis enables inclusion of all interactions within the variables and the exclusion of the share of the variance resulting from the variable noise. 

One advantage of multivariate correlation is the possibility of simultaneous handling of all variables in the time or local series. This enables all interactions within the variables in the series and between the series which are dependent upon lag to be taken into consideration. 

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