Multivariate time change analysis

What is the level of synchronisation between two phenomena or two features?

With multivariate analysis one can explore differences in evolution either between features or between phenomena for the same feature. When comparing the evolution of two features or two phenomena, behaviour differences correspond to non similar evolution trends or to a time-lag. When comparing time change, one should clearly identify the precise context of the analysis in order to select the most appropriate method:

• The richness of the time dimension: the time period is describe with simply two limits or with more details as a series of intervals constituting a time series.
• The level of measurement of the considered phenomena: nominal, ordinal or cardinal level. More simply as qualitative or quantitative data.
• The number of features or phenomena to be compared: with two, pairwise comparison methods (bivariate) can be chosen. With more than two, multiple comparison methods (multivariate) should be selected.

The following table lists 3 methods for multivariate analysis of the time dimension. One is used for comparing multiple features with several phenomena (variables) expressed at cardinal level but for only two time limits. The two remaining concern pairwise time series comparison adapted to qualitative or quantitative data.

The principle of the change vector analysis method (CVA) will be briefly describe, as cross-association and cross-correlation methods will be illustrated with more details in the following sections.