Bivariate Copula Fitting | Vose Software

# Bivariate Copula Fitting

### Introduction

With the Bivariate Copula Fit window, you can fit a bivariate copula to spreadsheet data.

The fitted distributions are ranked according to the SIC, AIC (Akaike) and HQIC For these holds: the lower an information criterion, the better the fit. To avoid confusion the negatives of these criteria are displayed in the list. This means that:

the higher the value shown in the list, the better the fit.

AIC and the other Information Criteria are superior goodness of fit statistics to other fit ranking criteria (e.g. chi-squared), because they take into account the number of parameters estimated, and penalize for overfitting: a model that has a good fit using fewer parameters is preferred over one that needs more parameters.

The AIC is the least strict of the three in penalizing for more parameters, while SIC is the strictest. More information on these can be found here.

When fitting a bivariate copula, the copula direction that best matches the data is chosen. If you do not want to vary the copula direction and just use the copula with the default direction, use multivariate copula fit instead.

Different types of output are possible, like the fitted parameters themselves, or data generated from the copula based on them.

### Window elements

When opening the Bivariate Copula Fit window, you are first asked to choose which copula(s) to fit. This selection can be changed any time later on.

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

Next shown is the list of Correlations (i.e. fitted copulas), ranked by SIC, AIC or HQIC criterion. Click one of these three to rank the fitted copulas according to it. Copulas for fitting can be added or removed for this list by pressing the add and remove buttons, respectively.

You can mark the check box to choose whether or not you want to include the (unavoidable) uncertainty in the fit. To read the motivation behind this parameter click here.

With the Chart mode buttons below the preview graph, you can switch between showing the source data, randomly generated data from the fitted copula, or a combination of both, as well as the number of generated points to be shown.

With the Output mode buttons below the preview graph, you can switch between exporting the parameters of the fitted copula, randomly generated values from the fitted copula, a combination of both or an object.

Industrial version only:

Clicking the “Create report” button  above the chart will produce a fit report in a new Worksheet with the fitted models in a table. The table will have the fitted Copula objects and Goodness of Fit rankings. The report will also include the OptimatFit function that automatically returns the best fitted model according to the selected information criteria.

An example of such report is available in the following  example model.

For explanations about other fields, buttons, graphs and summary statistics tables in this window, see