[R] Unable to manually replicate execution of a R function

[Brian Smith]

Hi,

** In may earlier post there were some typo, so reposting the same
after correction**

I am trying to replicate a function from rugarch package manually.
Below is the calculation based on the function,

library(rugarch)
data(dji30ret)
spec = ugarchspec(mean.model = list(armaOrder = c(1,1), include.mean = TRUE),
variance.model = list(model = "gjrGARCH"), distribution.model = "sstd")
fit = ugarchfit(spec, data = dji30ret[1:1000, 1, drop = FALSE])
spec2 = spec
setfixed(spec2)<-as.list(coef(fit))
filt = ugarchfilter(spec2, dji30ret[1001:2500, 1, drop = FALSE], n.old = 1000)
actual = dji30ret[1001:2500,1]
# location+scale invariance allows to use [mu + sigma*q(p,0,1,skew,shape)]
VaR = fitted(filt) + sigma(filt)*qdist("sstd", p=0.05, mu = 0, sigma = 1,
skew = coef(fit)["skew"], shape=coef(fit)["shape"])
alpha = 0.05
conf.level = 0.95

VaRDurTest(0.05, actual, VaR)$b ## 1.019356


Now I want to replicate the calculation manually as below,


VaR.ind = ifelse(actual < VaR, 1, 0)
N = sum(VaR.ind)
TN = length(VaR.ind)
D = diff(which(VaR.ind == 1))
C = rep(0, length(D))
N = length(D)

pweibull = function (D, a, b, survival = FALSE)
{
cdf = 1 - exp(-(a * D)^b)
if (survival)
cdf = 1 - cdf
return(cdf)
}
dweibull = function (D, a, b, log = FALSE)
{
pdf = (b * log(a) + log(b) + (b - 1) * log(D) - (a * D)^b)
if (!log)
pdf = exp(pdf)
return(pdf)
}
likDurationW = function (pars, D, C, N)
{
b = pars[1]
a = ((N - C[1] - C[N])/(sum(D^b)))^(1/b)
lik = C[1] * log(pweibull(D[1], a, b, survival = TRUE)) +
(1 - C[1]) * dweibull(D[1], a, b, log = TRUE) + sum(dweibull(D[2:(N -
1)], a, b, log = TRUE)) + C[N] * log(pweibull(D[N],
a, b, survival = TRUE)) + (1 - C[N]) * dweibull(D[N],
a, b, log = TRUE)
if (!is.finite(lik) || is.nan(lik))
lik = 10000000000
else lik = -lik
return(lik)
}
optim(par = 2, fn = likDurationW, gr = NULL, D = D, C = C, N = N,
method = "L-BFGS-B", lower = 0.001, upper = 10, control = list(trace =
0))$par  ## 1.029628

I fail to understand why there has to be a difference. Could you
please help to find the reason?

> sessionInfo()

R version 4.2.2 (2022-10-31)

Platform: x86_64-apple-darwin17.0 (64-bit)

Running under: macOS Big Sur ... 10.16


Matrix products: default

BLAS:   /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRblas.0.dylib

LAPACK: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRlapack.dylib


locale:

[1] C/UTF-8/C/C/C/C


attached base packages:

[1] parallel  stats     graphics  grDevices utils     datasets  methods

[8] base


other attached packages:

[1] rugarch_1.4-9


loaded via a namespace (and not attached):

 [1] Rcpp_1.0.9                  mclust_6.0.0

 [3] lattice_0.20-45             mvtnorm_1.1-3

 [5] zoo_1.8-12                  MASS_7.3-58.1

 [7] GeneralizedHyperbolic_0.8-4 truncnorm_1.0-9

 [9] grid_4.2.2                  pracma_2.4.2

[11] KernSmooth_2.23-20          SkewHyperbolic_0.4-0

[13] Matrix_1.5-1                xts_0.12.1

[15] spd_2.0-1                   tools_4.2.2

[17] ks_1.14.1                   numDeriv_2016.8-1.1

[19] compiler_4.2.2              DistributionUtils_0.6-1

[21] Rsolnp_1.16