I am estimating different copulas for bond factors that i also fit AR(1) models on.

Now i would like to test and compare durations and VaRs with my model vs empiric.

But how can i simulate AR(1) series with my copula properties? I can simulate both independently but i am unsure how to proceed to do both simulatneously

I hope my question isn't too specific.



1 Answer 1


As you know, simulating AR(1) is to simulate the distributed error path.

Assume the bivariate errors distributed $\sim F(x),\sim F(y)$ with copula $C(u,v)$ to model their dependence.

Then the bivariate joint error distribution is given by Sklar's theorem:


You can simulate from this distribution using Conditional Sampling:

To obtain a realization of a bivariate Copula $C(u,v)$, one draws the first variable $u$ as random number $\sim U(0,1)$. The second variable $v$ is generated from another independent random number $z$ plugged into the inverse Copula $C^{-1}(z\,|u=u)$ under the first generated (conditional) random number $u$:

  1. Draw $\bar{u},\bar{z}\sim U(0,1)$
  2. Set $\bar{v} = C_{\bar{u}}^{-1}(\bar{z})$ (quasi-inverse Copula under $\bar{u}$, or conditional $C^{-1}(t,u\,|u=\bar{u})$ )

From this you get $$(x=F(\bar{u})^{-1},y=F(\bar{v})^{-1})$$ as your two simulated errors for the AR(1) process.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.