Re: T Copula Calibration
- To: mathgroup at smc.vnet.net
- Subject: [mg78547] Re: [mg78530] T Copula Calibration
- From: Carl Woll <carlw at wolfram.com>
- Date: Wed, 4 Jul 2007 05:29:38 -0400 (EDT)
- References: <200707030944.FAA18997@smc.vnet.net>
dwstrickler at tx.rr.com wrote:
> All,
>
> In the interest of full disclosure and genuine humility, I don't code
> in Mathematica so much as I wrestle it into submission from time to
> time. Accordingly, I've come up against an optimization problem in
> which Mathematica flatly refuses to see things my way. In a nutshell,
> I have an n x 3 table of interdependent log-delta price data (to the
> extent it matters, I have a corresponding table of alpha-Stable
> standardized log-delta price data), and I'm trying to construct a
> simulation algorithm that will effectuate a Student T copula
> relationship between the three variables. (FWIW, I've managed to
> create Clayton and Gumbel copula RNGs for similar data; they work
> fine).
>
> The problem is the Student T copula density function, and in
> particular, the Student T DOF parameter, v. I've tried NMinimize,
> FindMinimum, and FindRoot, and I simply cannot get Mathematica to return a
> numerical value for v. In fact, the problem is broader than that - I
> can't get Mathematica to optimize ANY function that contains a Sum or
> Product
> term - but I digress.
>
> In terms of the density function, here's an example of what I've
> tried:
>
> tCopulaPDF[y__,v_,R_]:=Module[{dims,ret},dims=Length[Transpose[y]];ret=((Gamma
> [(v+dims)/2]*(Gamma[v/2])^dims-1)/(Gamma[(v+1)/
> 2]^dims)*(Det[R])^1/2)*NProduct[(1+
> (y[[i]]^2/v))^v+1/2,{i,1,dims}]*(1+y.R^-1*y/v)^-v+dims/2;Return[ret]];
^^^^^^
It's unnecessary to use Return here. Module automatically returns the
last expression.
Without creating data to test your code, I suspect that the problem is
that NMinimize attempts to evaluate tCopulaPDF with a symbolic v. If so,
the simple workaround is to use
tCopulaPDF[y_, v_?NumberQ, R_] := ...
If the above doesn't solve your problem, make sure that
tCopulaPDF[data, 1, corrmat]
evaluates to a number.
Another possible issue is the use of R^-1. Did you mean to use
Inverse[R] here instead?
Carl Woll
Wolfram Research
>
> where y is the n x 3 table, v is the DOF parameter, and R is the
> correlation matrix for y. Gamma[] is Mathematica's built-in Euler Gamma
> function.
>
> Then I try to optimize with something like:
>
> NMinimize[{tCopulaPDF[data,v,corrmat],v>0},v]
>
> No luck. Mathematica gives me the standard NAN warning, and then
> returns the
> function unevaluated.
>
> Thinking the source of the problem might be the NProduct term, I also
> tried expressing the density function a different way:
>
> tCopulaPDF[y__,v_,R_]:=Module[{dims,ret,cols,a,b,c},dims=Length[Transpose[y]];cols=y/.
> {a_,b_,c_}:>Apply[Times,(1+a^2/v)^v+1/2]+Apply[Times,(b^2/v)^v
> +1/2]+Apply[Times,(c^2/v)^v
> +1/2];ret=((Gamma[(v+dims)/2]*(Gamma[v/2])^dims-1)/(Gamma[(v+1)/
> 2]^dims)*(Det[R])^1/2)
> *cols*(1+y.R^-1*y/v)^-v+dims/2;Return[ret]];
>
> Same result. Any suggestions? I apologize in advance if the solution
> is blindingly obvious to everyone but me.
>
- References:
- T Copula Calibration
- From: dwstrickler@tx.rr.com
- T Copula Calibration