Simulation Master allows for the modeling of bivariate Archimedean copulas. Part of modeling a copula is to determine which copula to use, the direction of correlation, and the copula parameter, alpha. If there is data available, a copula can be fitted to the data. The fitting process automatically determines the best copula, its direction, and its alpha parameter.
To fit a copula, we need to two sets of data. Each set should be in columns in the Excel workbook. Both sets must also contain the same number of data points.
Click on the Fit Copula button on the ribbon.
The Fit Copula form will appear.
Variable 1 & 2 Data to Fit
For each data to fit box, enter the cell range for each data set. You can type a valid cell range in each box, or you can use the minimize button next to each box and select the ranges in the worksheet. For variable 1, the data resides in the range D2:D1001. Variable 2 data resides in E2:E1001.
Copulas are fitted using maximum likelihood estimation. To do this, the software must numerically find the best solution for each copula. The intensity setting determines how long the software will search for a solution. In most cases, the normal setting should be used.
Copulas to Fit
Select any copulas that you want the software to attempt to fit. Simulation Master can fit four copula types:
- Farlie-Gumbel-Morgenstern (FGM)
The number at the end of each copula name refers to the direction of correlation. To learn more about copula directions, refer to this page.
We will fit all of the Clayton copulas for this tutorial.
Once everything has been entered, click the Fit Data button.
Once the fitting process is complete the Copula Fit Results form will appear.
Copula fits are ranked using information criteria. There are three information criteria calculated:
- Bayesian Information Criterion (BIC)
- Aikake Information Criterion (AIC)
- Hannan-Quinn Information Criterion (HQIC)
A lower information criterion value indicates a better relative fit. In our example, the Clayton 1 has the lowest value for all three information criteria (largest negative number), and is therefore the best fit among the original four copulas that we selected for fitting.
A given information criterion does not say anything about how well a copula fits the data, it is only used as a comparison relative to other candidate copulas.
Create a Fit Report
A fit report can be created by clicking on the Create Report button. The Copula Fit Reports form will appear.
We will create a report for Clayton 1 and the report will be located in the current workbook. The report for Clayton 1 is shown below.
Write to Cells
You can write copula functions to cells in a worksheet with the Write to Cells button. Click on the button and you will be prompted to select the upper left cell where the functions will be written. We will select cell G5 on a worksheet.
There will be four cells that will contain the functions required to create a copula. Two of the cells contain the copula functions (one for each variable) and two that generate random numbers using the RANDNUM( ) function. The functions in the worksheet are shown below. Note that formulas are shown to illustrate what is written to the cells. The cell values are numeric.
For more information on copula functions and their parameters, refer to the Simulation Master Premium User Manual.