CCOPULA Procedure

This example analyzes the dependencies among the market sectors in the S&P 500 index. The S&P 500 index consists of 11 sectors: Information Technology, Health Care, Financials, Consumer Discretionary, Communication Services, Industrials, Consumer Staples, Energy, Utilities, Real Estate, and Materials. This analysis considers daily returns for these sectors that have been corrected for stock splits and dividend payments over the years 1999 to 2020.

To facilitate visualization of the return data, this analysis is limited to the Utilities, Consumer Discretionary, Industrials, and Financials sectors. The following code fits a t copula and performs a simulation of the estimated t copula:

/* PROC CCOPULA visualization of sector returns */
proc ccopula data=mylib.sectret;
   var utilities discretionary industrial financial;
   fit t / marginals=empirical plots(tail kendall)=(datatype=uniform)
           store=mylib.sectstor;
   simulate / seed=1 ndraws=5635 outuniform=mylib.ou
              plots(tail kendall)=(datatype=uniform);
run;

Output 8.3.1 compares the tail plots of the actual return data to plots of the simulated data. Both plots show similar patterns for the dependencies among the various sectors. In particular, the Utilities sector appears to have a consistently low correlation with the other sectors for returns near the mean and for both the high and low extreme values. For the other three sectors, higher correlations are apparent among the returns. Based on the correlation and tail plots in Output 8.3.1, you would be likely to conclude that the estimated t copula represents the dependencies among returns well.

Output 8.3.1: Actual (Upper) and Simulated (Lower) Tail Plots

Output 8.3.2 compares the Kendall plots of the actual return data to plots of the simulated data. The Kendall plots for these sectors show that the t copula models the range of returns well. Plots of both the observed and simulated data relative to a uniform bivariate distributions show similar patterns.

Output 8.3.2: Actual (Upper) and Simulated (Lower) Kendall Plots