Estimating BB1 Copula Parameters for a Goodness-of-Fit Test

Summary

The document explains how to pass parameters to a two-dimensional BB1 copula when running a goodness-of-fit test in R. The reported issue is that the BB1 constructor does not accept a dimension argument in the same way as the normal copula constructor used for comparison. The suggested approach supplies the two fitted BB1 parameters directly to the constructor, then uses that copula object with the test and the bivariate data.

The parameters are taken from a previously selected copula model: one for the first dependence parameter and one for the second. This is a practical usage note rather than a full estimation procedure. It does not explain how model selection works, how the parameters are estimated, what goodness-of-fit statistic is used, or how to interpret the test result. The example also gives no validation or comparison of alternative fitting approaches.

Key ideas

• The BB1 constructor is shown receiving its two parameters as a pair rather than a dimension argument.
• The suggested goodness-of-fit workflow uses parameters from a previously selected copula model.
• The note does not describe parameter estimation or how to interpret the goodness-of-fit output.

Tags

# What is the R code for estimating copula parameters of BB1 with dim=2? And what's the code for gof test of BB1?


# What is the R code for estimating copula parameters of BB1 with dim=2? And what's the code for gof test of BB1?












Kindly assist with R code for BB1 copula. Text books and research articles provide codes for clayton, gumbel, frank, normal and t copulas. However, I can't find code for BB1, the copula family defined in `H. Joe: Multivariate Models and Multivariate Dependence Concepts, Chapman & Hall, 1997, p. 150`

For example, this is the code I found:

```
gf <- gofCopula(normalCopula(dim = 2), as.matrix(mydata), N = 50). ## I obtained results here
```

But I get an error when I run:

```
gfBB1 <- gofCopula(BB1Copula(dim = 2), as.matrix(mydata), N = 50)
```

> Error in BB1Copula(dim = 2) : unused argument (dim = 2)

## Answer by user44687 (score 1)

https://quant.stackexchange.com/a/51552

I have just found out what the code is. Note that theta and delta come from the copula selected for you through the BiCopSelect() command.

```
theta <- selectedCopula$par
delta <- selectedCopula$par2

gfBB1 <- gofCopula(BB1Copula(c(theta, delta)), as.matrix(mydata), N = 50)
```

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.