Defining a Correlation Matrix

You can specify correlations between members of the Stochastic or History Generator An element that generates stochastic time histories of variables. A stochastic time history is a random time history that is generated according to a specified set of statistics. vector A one-dimensional array. via a correlation matrix A two-dimensional array.. A correlation matrix specifies the correlations between variables, and generally has the following form:

Note that by definition, a correlation matrix is symmetric around its diagonal (since the cross diagonal terms define the same correlation coefficient).

By default, all off-diagonal correlation coefficients are zero. The matrix is symmetrical, so you need only define one of the cross-diagonal terms. The value represents a rank correlation coefficient, and must vary between -1 and 1. It must be a number (i.e., you cannot specify a link).

Note: When you define a correlation matrix, it is important to ensure that it is internally consistent. For example, if you specified that A was positively correlated to B, and B was positively correlated to C, but that A was negatively correlated to C, the correlation matrix would be inconsistent (since in this case, A should also be positively correlated to C). When this occurs, GoldSim will produce a fatal error message.

GoldSim provides several different algorithms for correlating the members of the vector. These are selected from the Correlation Algorithm drop-list at the top of the dialog. The various correlations algorithms are discussed in detail in Appendix B of the GoldSim User’s Guide.