kupiec-methods function

Method to backtest VaR violation using the Kupiec statistics

An S4 method that performs backtest for VaR models using the Kupiec statistics. For a sample of $n$ observations, the Kupiec test statistics takes the form of likelihood ratio

c("$LR_{PoF}= -2 \\log\\left(\\frac{(1-\\alpha)^{T-n_f}\\alpha^{n_f}}\n$", "${\\left(1-\\frac{n_f}{T}\\right)^{T-n_f}\\left(\\frac{n_f}{T}\\right)^{n_f}}\\right)$")

c("$LR_{TFF}= -2 \\log\\left\n$", " (\\frac{\\alpha(1-\\alpha)^{t_f -1}} {\\left ( \\frac{1}{t_f}\\right\n", " )\\left ( 1- \\frac{1}{t_f}\\right )^{t_f-1}}\\right),\n")

where $n_f$ denotes the number of failures occurred and $t_f$ the number of days until the first failure within the $n$

observations. Under $H_0$, both $LR_{PoF}$ and $LR_{TFF}$ are asymptotically $\chi^2_1$-distributed, and their exceedance of the critical value implies that the VaR model is inadequate. methods

kupiec(y, VaR, VaR_level, verbose = TRUE, test = "PoF")

## S4 method for signature 'ANY'
kupiec(y, VaR, VaR_level, verbose = TRUE, test = "PoF")

Arguments

• y: The time series to apply a VaR model (a single asset rerurn or portfolio return).
• VaR: The forecast VaR.
• VaR_level: The VaR level, typically 95% or 99%.
• verbose: If TRUE show the outcome. Default is TRUE.
• test: Choose between PoF or TFF. Default is PoF.

Examples

pw.CCC.obj = new("simMGarch")
pw.CCC.obj@d = 10
pw.CCC.obj@n = 1000
pw.CCC.obj@changepoints = c(250,750)
pw.CCC.obj = pc_cccsim(pw.CCC.obj)
y_out_of_sample = t(pw.CCC.obj@y[,900:1000])
w=rep(1/pw.CCC.obj@d,pw.CCC.obj@d) #an equally weighted portfolio
#VaR = quantile(t(pw.CCC.obj@y[,1:899])%*%w,0.05)
#ts.plot(y_out_of_sample%*%w,ylab="portfolio return");abline(h=VaR,col="red")
#kupiec(y_out_of_sample%*%w,rep(VaR,100),.95,verbose=TRUE,test="PoF")

References

Kupiec, P. "Techniques for Verifying the Accuracy of Risk Management Models." Journal of Derivatives. Vol. 3, 1995, pp. 73–84.