topic Re: Copula Based Non-linear Regression in SAS Procedures

Copula Based Non-linear Regression

sara_a — Fri, 24 Jul 2015 20:55:09 GMT

Hi everyone and Happy Friday,

I'm working with data that does not have a normal distribution nor do response/explanatory variables have a linear relationship. I came across the concept of CQR (copula quantile regression) that doesn't seem to require the assumptions that regular linear regression require. Is there a way to do CQR in SAS? I know there's proc quantreg but I thought that only works for a linear quantile regression. Suggestions?

Thanks!

Re: Copula Based Non-linear Regression

Ksharp — Sat, 25 Jul 2015 13:07:13 GMT

Not sure.

You could try PROC LASS which can do nonparameter regression .No need Data Distribution,No need Link Function.

Xia Keshan

Re: Copula Based Non-linear Regression

SteveDenham — Mon, 27 Jul 2015 12:39:39 GMT

Hey xia--did you mean PROC LOESS?

Also, if the original poster has SAS/ETS installed, then PROC COPULA may be of interest. Quantile estimates are obtained by multi-stage analyses, as outlined in Example 10.1 Copula Based VaR Estimation, which gives quantile estimates via PROC UNIVARIATE after a fair amount of pre-processing using PROC COPULA.

Steve Denham

Re: Copula Based Non-linear Regression

Ksharp — Mon, 27 Jul 2015 12:42:39 GMT

Yeah, Steve it is LOESS. I got confused .

Re: Copula Based Non-linear Regression

Rick_SAS — Tue, 28 Jul 2015 17:55:05 GMT

Steve,

You make an interesting observation. I didn't think that PROC COPULA could handle regression-type problems (which have a response variable). The FIT statement fits the parameters of a copula to model the joint distribution function of the variables, and I never considered looking at conditional means or quantiles of the response, given the other variables.

I found an interesting paper http://www.variancejournal.org/issues/05-01/45.pdf (Parsa and Klugman, 2011) in which the authors mention that they use SAS/IML for the optimization and for some numerical integration that must be performed for the generalized linear model regression example.

The authors provide some simulated data and examples.The motivated SAS/IML programmer could probably replicate their examples.

Re: Copula Based Non-linear Regression

SteveDenham — Tue, 28 Jul 2015 17:59:52 GMT

I think the key to using PROC COPULA is to get away from thinking of independent and dependent variables--just a joint distribution. Once you take that step, what is given in the VaR estimation example is pretty straightforward (at least compared to time-dependent copulas that the financial guys are modeling these days).

Steve Denham