Copula functions, R, and the financial crisis

r copula graphs.r

# *------------------------------------------------------------------
# | PROGRAM NAME: R_COPULA_BASIC
# | DATE: 1/25/11
# | CREATED BY: Matt Bogard 
# | PROJECT FILE: http://econometricsense.blogspot.com/2011/03/copula-functions-r-and-financial-crisis.html           
# *----------------------------------------------------------------
# | PURPOSE:    copula graphics           
# | 
# *------------------------------------------------------------------
# | COMMENTS:               
# |
# |  1: REFERENCES:  Emjoy the Joy of Copulas: With a Package copula
# |     Journal of Statistical Software Oct 2007, vol 21 Issue 1
# |      http://www.jstatsoft.org/v21/i04/paper 
# |  2: 
# |  3: 
# |*------------------------------------------------------------------
# | DATA USED:               
# |
# |
# |*------------------------------------------------------------------
# | CONTENTS:               
# |
# |  PART 1:  
# |  PART 2: 
# |  PART 3: 
# *-----------------------------------------------------------------
# | UPDATES:               
# |
# |
# *------------------------------------------------------------------
 
 
library("copula")
set.seed(1)
 
# *------------------------------------------------------------------
# |                
# |scatterplots
# |  
# |  
# *-----------------------------------------------------------------
 
 
# normal (Gausian?) Copula
 
norm.cop <- normalCopula(2, dim =3)
norm.cop
x <- rcopula(norm.cop, 500)
plot(x)
title("Gaussian Copula")
 
# Clayton Copula
 
clayton.cop <- claytonCopula(2, dim = 2)
clayton.cop
y <- rcopula(clayton.cop,500)
plot(y)
title("Clayton Copula")
 
# Frank Copula
 
frank.cop <- frankCopula(2, dim = 2)
frank.cop
f <- rcopula(frank.cop,500)
plot(f)
title("Frank Copula")
 
 
# Gumbel Copula
 
gumbel.cop <- gumbelCopula(2, dim = 2)
gumbel.cop
g <- rcopula(gumbel.cop,500) 
plot(g)
title('Gumbel Copula')
 
# *------------------------------------------------------------------
# |                
# |  contour plots 
# |  
# |  
# *-----------------------------------------------------------------
 
 
# clayton copula contour
myMvd1 <- mvdc(copula = archmCopula(family = "clayton", param = 2),
margins = c("norm", "norm"), paramMargins = list(list(mean = 0,
sd = 1), list(mean = 0, sd = 1)))
 
contour(myMvd1, dmvdc, xlim = c(-3, 3), ylim = c(-3, 3))
title("Clayton Copula")
 
# frank copula contour
myMvd2 <- mvdc(copula = archmCopula(family = "frank", param = 5.736),
margins = c("norm", "norm"), paramMargins = list(list(mean = 0,
sd = 1), list(mean = 0, sd = 1)))
 
contour(myMvd2, dmvdc, xlim = c(-3, 3), ylim = c(-3, 3))
title("Frank Copula")
 
# gumbel copula 
myMvd3 <- mvdc(copula = archmCopula(family = "gumbel", param = 2),
margins = c("norm", "norm"), paramMargins = list(list(mean = 0,
sd = 1), list(mean = 0, sd = 1)))
 
contour(myMvd3, dmvdc, xlim = c(-3, 3), ylim = c(-3, 3))
title("Gumbel Copula")