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I am working with time-varying normal copulas who equation is given by

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The dynamic equation of dependence parameter $\rho$ is :

enter image description here

Where $u_1=F_1 (ε_{1,t} )$ and $u_2=F_2 (ε_{2,t} ) $

I found the values of the parameters as follows:-

My $ω_N=0.0433$ $ β_N=-0.1718$ and $α_N=0.6016$ and $ρ_0= -0.0699$.

I now need to generate a vector of ($\hat{ε_{1,t}}$ ) ̂ and ($\hat{ε_{2,t}}$ ) for forecasting and comparing models. How do I generate them in Excel or R.

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