Fit Copula

Similar to input distributions, a copula can be fit to an existing data set (a correlation does not require fitting as it always utilizes the elliptical gaussian type). The fitted copula configuration can then be used with other inputs.

The fitting process must include at least two columns of data (two sets of data to be correlated); when the fitting process runs, @RISK will test each of the selected copula types against the data to determine which copula would reproduce sample values most similar to the existing data. Once the fitting process is complete, @RISK will display the results in the Copula Fit Results window.

To fit a copula to an existing set of data, select at least two columns of values, click the lower half of the Correlations button, and select Fit Copula.

Figure 1 - Fit Copulas to Data Window

Fit Copulas to Data

The Fit Copulas to Data window consists of the following primary sections:

  1. Data Set - Details of the data to be to be included in the fit. See below for more information.
  2. Fitting - Configurations for the method of fitting and the copula types to be tested.
  3. Command Buttons

Data Set

The Data Set panel includes the details of the data set to be used in the fitting process.

  • Range - The cell range containing the values to be used in the fitting process.
  • Variable Names in First Row - Check this box if the selected cell range includes column headers or labels.
  • Data Already Demarginalized - Check this box if the selected data has already been demarginalized. If this is left unchecked, @RISK will demarginalize the data set before running the fit.

Fitting

The fitting process uses the selected data set and tests all copula types that have been selected for fitting against the data. The method for determining how well a copula fits to the data can also be selected.

When using any of the fitting methods, select the copula types to be tested by checking the box next to the copula name.

Select a fitting method from the Method pull-down menu. The options include:

  • Maximum Likelihood Estimation (High Accuracy) - With Maximum Likelihood Estimation (MLE), the parameters of each fitted copula type are chosen to maximize the joint likelihood function of observing the given sample data. Please note: the High Accuracy method will take longer to complete, especially with larger sample data sets.
  • Maximum Likelihood Estimation (Approximate) - With Maximum Likelihood Estimation (MLE), the parameters of each fitted copula type are chosen to maximize the joint likelihood function of observing the given sample data. The Approximate method sacrifices some accuracy, but can be used with a greater number of sample data points.
  • Kendall's Tau Inversion - Each pair of variables have their Kendall's Tau statistic calculated (measuring how often the variables both move in the same direction - up or down), and the parameters for each of the fitted copula types are matched to give the same theoretical statistic. The Kendall Tau Inversion method can be used with very large sample data sets and is much faster than MLE; however, its convergence is slower, requiring more data points to achieve the same accuracy as MLE.

Command Buttons

The Command Buttons of the Fit Copulas to Data window include:

  • Help - Open help resources (online or local, based on @RISK settings); the Help Button for more information.
  • Settings/Actions - Window-specific seettings and actions. The Fit Copulas to Data options are:
    • Load Fit From File - If a copula fit has previously been run, or has been run in a separate model, and the results exported as a CFT file, the results of the fit can be loaded from that export. See Copula Fit Results for more information.