MannWhitney.Wilcoxon <- function(met=1, DGP=1:15, mets=7, res=2, replic=1000)
{
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#                                                                              #
#    Mann-Whitney and Wilcoxon Function by Breno de Andrade Pinheiro Néri      #
#                                                                              #
#            brenoneri@gmail.com        www.fgv.br/aluno/bneri                 #
#                                                                              #
#                                                    October, 2005 - Version 2 #
#                                                                              #
################################################################################
#                                                                              #
# This code computes Mann-Whitney and Wilcoxon test to help you to analyze the #
# results of the Monte Carlo Simulations generated by MC_VaR.R or MC_VaRox.R.  #
#                                                                              #
# You enter the VaR methodology (met), the DGP range (DGP, observe that it is  #
# a vector), the number of                                                     #
# methodologies generated in your Monte Carlo Simulations (mets), the desired  #
# test statistics (res) and the number                                         #
# of replications generated in your MC Simulations (replic).                   #
#                                                                              #
# You can choose among eleven test statistics generated by the code            #
# BackTest.R, setting up the res variable. Namely:                             #
# 1: frequency of violations;                                                  #
# 2: number of violations (default);                                           #
# 3: ---Not Available---;                                                      #
# 4: Unconditional Coverage (Kupiec, 1995) Likelihood Ratio Test;              #
# 5: Independence (Christoffersen, 1997) Likelihood Ratio Test;                #
# 6: Conditional Coverage (Christoffersen, 1997) Likelihood Ratio Test;        #
# 7: Dynamic Quantile (Engle and Manganelli, 2002) Test Statistic;             #
# 8: Unconditional Coverage (Kupiec, 1995) P-Value;                            #
# 9: Independence (Christoffersen, 1997) P-Value;                              #
# 10: Conditional Coverage (Christoffersen, 1997) P-Value;                     #
# 11: Dynamic Quantile (Engle and Manganelli, 2002) P-Value;                   #
# 12: Magnitude Loss Function (Lopez, 1998).                                   #
#                                                                              #
# Defaults: met=1, DGP=1:15, mets=7, res=2, replic=1000.                       #
#                                                                              #
################################################################################
#                                                                              #
# You may use this code only if you accept the conditions:                     #
# (1) I am not liable for any problem caused by this code (i.e. you use it at  #
# your own risk);                                                              #
# (2) You must give me credit in your papers where this code has been used.    #
#                                                                              #
################################################################################

message("")
message("Two sided Mann-Whitney and Wilcoxon rank sum test with continuity correction p-values:")
for(j in DGP)
{
    x <- array(0, c(replic, mets))
    for(i in 1:replic)
    {
        load(paste("MC_VaR", j, i, "R", sep="."))
        x[i,] <- result[[res]]
    }
    message("")
    message("VaR methodology ", met, " under DGP ", j, ":")
    for(i in 1:mets) message("Comparing with VaR methodology ", i, ": ", wilcox.test(x[,met], x[,i], alternative="two.sided")[[3]])
}
}