Empirical Copula

See also: ModelRisk functions and windows, Copulas in ModelRisk, Copulas, Distribution functions and the U parameter

Introduction

 

The Empirical Copula window provides a way to directly  construct a bivariate or multivariate copula based on spreadsheet data. From this constructed copula, randomly sampled values can be generated.

Note the difference between constructing an empirical copula, and fitting an existing type of copula:

When fitting a copula, we determine the parameter of the copula that makes for a best fit to the data, but retaining the copula's functional form. With the empirical copula, the functional form itself (not just the parameter) is based on the data, making it a flexible tool for capturing any correlation pattern, however unusual.

From within this window, you can also specify the distributions that model the variables to be correlated by this empirical copula, as well as names for these variables, and insert these in the spreadsheet.

You can read more about the mathematical details of copulas here.

To see the output functions of this window, click here.

Window elements

In the Source data region, the location of the source data in the spreadsheet, and its orientation (in rows or columns) can be selected.

Uncertainty in constructing the empirical copula can be included by marking the check box.

In the Variables references region, you can (optionally) select distributions to model the variables that will be correlated by the empirical copula. If you select none, randomly generated values from the constructed copula will be outputted. You can of course always link these to distributions in your spreadsheet model through the U-parameter later on.

To select a distribution to model one of the correlated variables, first click this variable's label in the correlation matrix shown, then fill in the desired VoseDistribution in the Distribution for current variable field.

For the preview graph, you can choose between displaying generated percentiles (i.e. copula values) or randomly sampled values of the correlated variables (if you selected a distribution for them as explained above).

You can specify the number of Fitted points in the designated field.

With the Chart mode buttons you can choose wether to display source data, the constructed empirical copula or a combination of both.

For explanations about other fields, buttons, graphs and summary statistics tables in this window, see Common elements of ModelRisk windows.

Useful tips and tricks

See also: Graphics, workflow and error handling in ModelRisk

Using View Function to return to a window

The output of ModelRisk windows always corresponds to VoseFunctions (the functions ModelRisk adds to Excel) being entered into one or more spreadsheet cells.

You can always re-open the window for a ModelRisk function that is in a spreadsheet cell by using View Function. Select the spreadsheet cell and then select View Function from the ModelRisk menu/toolbar/ribbon.


 

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