A History Generator can be specified to represent a 1-D array of variables (i.e., a vector). In this case, the various input parameters must be specified as vectors.
This most common application of this is to simulate an array of correlated variables (e.g., a portfolio of investments). When variables are correlated, their random movements (as typically quantified by the volatility) are linked to a greater or lesser degree. For example, consider the three time series below:
In this example, the volatile movements of Beta and Gamma are strongly correlated, and are both uncorrelated to Alpha.
The correlations between the members of an array are specified via a correlation matrix. 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).
If you specify that the History Generator represents a 1-D array of variables (i.e., a vector), then the Use correlation matrix checkbox becomes available on the History Generator dialog:
If this box is checked, the Edit Matrix… button becomes available. This button provides access to a dialog for specifying the correlation matrix:
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.