library(quantmod)
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library(timeDate)
library(writexl)
library(moments)
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library(evir)
library(dplyr)
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library(lubridate)
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library(xts)
library(ggplot2)
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library(evmix)
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library(tidyr)
library(scales)
library(eva)
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library(extRemes)
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library(gnFit)
# 1. MENGAMBIL DATA SAHAM DARI YAHOO FINANCE ------------------------------
Saham <- c("BBCA.JK", "BBNI.JK", "BBRI.JK", "BMRI.JK", "BRIS.JK")
getSymbols(Saham, from = "2019-05-01", to = "2025-05-31")
## [1] "BBCA.JK" "BBNI.JK" "BBRI.JK" "BMRI.JK" "BRIS.JK"
AdjCloses <- merge(
Ad(BBCA.JK), Ad(BBNI.JK), Ad(BBRI.JK), Ad(BMRI.JK), Ad(BRIS.JK)
)
colnames(AdjCloses) <- c("BBCA", "BBNI", "BBRI", "BMRI", "BRIS")
AdjCloses <- na.omit(AdjCloses[isWeekday(index(AdjCloses)), ])
head(AdjCloses)
## BBCA BBNI BBRI BMRI BRIS
## 2019-05-01 4746.710 3426.592 2564.676 2434.270 512.6640
## 2019-05-02 4693.052 3364.127 2564.676 2426.392 508.0455
## 2019-05-03 4684.797 3301.663 2570.545 2410.636 503.4269
## 2019-05-06 4639.395 3167.812 2482.512 2371.247 498.8083
## 2019-05-07 4672.415 3194.583 2494.250 2410.636 498.8083
## 2019-05-08 4705.435 3123.195 2476.644 2371.247 494.1897
tail(AdjCloses)
## BBCA BBNI BBRI BMRI BRIS
## 2025-05-21 9232.149 4160.240 3856.164 4907.147 2855.322
## 2025-05-22 9184.562 4114.219 3892.372 4907.147 2845.577
## 2025-05-23 9208.355 4151.036 3937.632 4884.638 2865.067
## 2025-05-26 9160.767 4141.832 3910.476 4929.657 2884.557
## 2025-05-27 8994.208 4169.444 3955.736 4862.128 2897.109
## 2025-05-28 8946.619 4132.627 4028.153 4772.088 2946.213
View(AdjCloses)
# 2. MENGHITUNG LOG RETURN MASING-MASING SAHAM ----------------------------
LogReturns <- na.omit(merge(
dailyReturn(Ad(BBCA.JK), type = "log"),
dailyReturn(Ad(BBNI.JK), type = "log"),
dailyReturn(Ad(BBRI.JK), type = "log"),
dailyReturn(Ad(BMRI.JK), type = "log"),
dailyReturn(Ad(BRIS.JK), type = "log")
))
colnames(LogReturns) <- c("BBCA","BBNI","BBRI","BMRI","BRIS")
LogReturns <- na.omit(LogReturns)
head(LogReturns)
## BBCA BBNI BBRI BMRI BRIS
## 2019-05-01 0.000000000 0.00000000 0.000000000 0.000000000 0.000000000
## 2019-05-02 -0.011368569 -0.01839743 0.000000000 -0.003241407 -0.009049649
## 2019-05-03 -0.001760507 -0.01874224 0.002285553 -0.006514810 -0.009132536
## 2019-05-06 -0.009738794 -0.04138525 -0.034846779 -0.016474807 -0.009216586
## 2019-05-07 0.007092208 0.00841528 0.004717049 0.016474807 0.000000000
## 2019-05-08 0.007042159 -0.02259980 -0.007083845 -0.016474807 -0.009302384
tail(LogReturns)
## BBCA BBNI BBRI BMRI BRIS
## 2025-05-21 0.023469097 0.015607951 0.011806542 0.009216620 0.010291677
## 2025-05-22 -0.005167915 -0.011123623 0.009345835 0.000000000 -0.003418718
## 2025-05-23 0.002587296 0.008908775 0.011560851 -0.004597692 0.006825873
## 2025-05-26 -0.005181410 -0.002219764 -0.006920485 0.009174342 0.006779766
## 2025-05-27 -0.018349050 0.006644565 0.011507636 -0.013793270 0.004342008
## 2025-05-28 -0.005305104 -0.008869268 0.018141096 -0.018692163 0.016807107
View(LogReturns)
# 3. ANALISIS DESKRIPTIF RETURN SAHAM -------------------------------------
DeskriptifReturnSaham <- data.frame(
Mean = apply(LogReturns, 2, mean, na.rm = TRUE),
Min = apply(LogReturns, 2, min, na.rm = TRUE),
Max = apply(LogReturns, 2, max, na.rm = TRUE),
SD = apply(LogReturns, 2, sd, na.rm = TRUE),
Variance = apply(LogReturns, 2, var, na.rm = TRUE),
Skewness = apply(LogReturns, 2, function(x) moments::skewness(x, na.rm = TRUE)),
Kurtosis = apply(LogReturns, 2, function(x) moments::kurtosis(x, na.rm = TRUE))
)
DeskriptifReturnSaham <- DeskriptifReturnSaham %>%
mutate(
Mean = round(Mean, 6),
Min = round(Min, 6),
Max = round(Max, 6),
SD = round(SD, 6),
Variance = round(Variance, 6),
Skewness = round(Skewness, 3),
Kurtosis = round(Kurtosis, 3)
)
print(DeskriptifReturnSaham)
## Mean Min Max SD Variance Skewness Kurtosis
## BBCA 0.000430 -0.089153 0.159849 0.015871 0.000252 0.571 12.774
## BBNI 0.000127 -0.124642 0.127927 0.021943 0.000481 0.151 7.115
## BBRI 0.000306 -0.106733 0.186411 0.020970 0.000440 0.482 9.499
## BMRI 0.000457 -0.139172 0.146721 0.021503 0.000462 -0.049 8.119
## BRIS 0.001186 -0.155485 0.223144 0.035342 0.001249 2.017 14.258
Datareturn <- data.frame(
Tanggal = index(LogReturns),
coredata(LogReturns)
)
Data_Long <- Datareturn %>%
dplyr::select(Tanggal, BBCA, BBNI, BBRI, BMRI, BRIS) %>%
pivot_longer(
cols = -Tanggal,
names_to = "Saham",
values_to = "Return"
)
# Plot Time Series Return
PlotReturn <- ggplot(Data_Long, aes(x = Tanggal, y = Return, color = Saham)) +
geom_line(linewidth = 0.5, alpha = 0.8) +
facet_wrap(~ Saham, ncol = 2) +
labs(
x = "Year",
y = "Log Return"
) +
theme_minimal(base_size = 12) +
theme(
legend.position = "none",
plot.title = element_text(face = "bold"),
strip.text = element_text(face = "bold", size = 12)
) +
scale_color_brewer(palette = "Set1")
print(PlotReturn)
# Plot Distribusi
PlotDistribusi <- ggplot(Data_Long, aes(x = Return)) +
geom_histogram(aes(y = after_stat(density), fill = Saham),
color = "white",
bins = 45,
alpha = 0.7) +
geom_density(color = "midnightblue", linewidth = 0.8) + facet_wrap(~Saham, scales = "free") +
labs(
title = "Distribusi Log Return Harian",
subtitle = "Periode 1 Mei 2019 - 31 Mei 2025",
x = "Log Return",
y = "Density",
fill = "Kode Saham"
) +
theme_minimal(base_size = 12) +
theme(
legend.position = "bottom",
plot.title = element_text(face = "bold", size = 14),
strip.text = element_text(face = "bold", size = 11),
panel.grid.minor = element_blank()
) +
scale_fill_brewer(palette = "Set2")
print(PlotDistribusi)
# A. UJI STATISTIK: SHAPIRO-WILK
UjiNormalitas <- data.frame(
Saham = colnames(LogReturns),
W_Statistic = numeric(ncol(LogReturns)),
P_Value = numeric(ncol(LogReturns))
)
for (i in 1:ncol(LogReturns)) {
data_saham <- as.numeric(LogReturns[, i])
uji <- shapiro.test(data_saham)
UjiNormalitas$W_Statistic[i] <- round(uji$statistic, 4)
UjiNormalitas$P_Value[i] <- uji$p.value
}
print(UjiNormalitas)
## Saham W_Statistic P_Value
## 1 BBCA 0.9260 2.405679e-26
## 2 BBNI 0.9469 1.270328e-22
## 3 BBRI 0.9399 5.469911e-24
## 4 BMRI 0.9426 1.807316e-23
## 5 BRIS 0.8228 1.564958e-37
# 4. MENENTUKAN BOBOT MASING MASING SAHAM ---------------------------------
meanreturn <- colMeans(LogReturns)
bobot <- as.numeric(meanreturn / sum(meanreturn))
names(bobot) <- colnames(LogReturns)
hasil <- data.frame(
Aset = names(bobot),
Mean_Return = round(as.numeric(meanreturn), 6),
Bobot = round(bobot, 4),
Bobot_Persen = round(bobot * 100, 2)
)
print(hasil)
## Aset Mean_Return Bobot Bobot_Persen
## BBCA BBCA 0.000430 0.1716 17.16
## BBNI BBNI 0.000127 0.0507 5.07
## BBRI BBRI 0.000306 0.1222 12.22
## BMRI BMRI 0.000457 0.1822 18.22
## BRIS BRIS 0.001186 0.4733 47.33
# 5. MENGHITUNG RETURN PORTOFOLIO ------------------------------------------
logreturns <- as.matrix(LogReturns)
Rp <- as.numeric(logreturns %*% matrix(bobot, ncol = 1))
ReturnPortofolio <- data.frame(
Tanggal = index(LogReturns),
Return = Rp
)
ReturnPortofolio$Loss <- -1 * ReturnPortofolio$Return
View(ReturnPortofolio)
# 6. BLOCK MAXIMA-------------------------------
ReturnPortofolio$Tanggal <- as.Date(ReturnPortofolio$Tanggal)
BlockMaxima <- ReturnPortofolio %>%
arrange(Tanggal) %>%
mutate(
BlockID = ceiling(row_number() / 15)
) %>%
group_by(BlockID) %>%
slice_max(order_by = Loss, n = 1, with_ties = FALSE) %>%
ungroup() %>%
dplyr::select(Tanggal, Loss) %>%
rename(Max_Loss = Loss)
BlockMaxima <- na.omit(BlockMaxima)
BlockMaxima <- BlockMaxima[is.finite(BlockMaxima$Max_Loss), ]
head(BlockMaxima)
## # A tibble: 6 × 2
## Tanggal Max_Loss
## <date> <dbl>
## 1 2019-05-14 0.0164
## 2 2019-05-28 0.0184
## 3 2019-06-26 0.0103
## 4 2019-07-05 0.0106
## 5 2019-08-05 0.0284
## 6 2019-09-02 0.0336
tail(BlockMaxima)
## # A tibble: 6 × 2
## Tanggal Max_Loss
## <date> <dbl>
## 1 2025-02-06 0.0368
## 2 2025-02-27 0.0625
## 3 2025-03-20 0.0535
## 4 2025-04-08 0.106
## 5 2025-05-08 0.0408
## 6 2025-05-27 0.00186
View(BlockMaxima)
write_xlsx(BlockMaxima, "C:/Users/Asus/OneDrive/문서/BISMILLAH SKRIPSI/DATA/BlockMaxima2.xlsx")
# 7. PEAK OVER THRESHOLD (POT) ---------------------------------------------
port_loss <- ReturnPortofolio$Loss
# 1. Urutkan Data dari Terbesar ke Terkecil
loss_sorted <- sort(port_loss, decreasing = TRUE)
n_total <- length(loss_sorted)
jumlah_ekstrem <- floor(0.10 * n_total)
# 3. Tentukan Threshold
threshold_u <- loss_sorted[jumlah_ekstrem]
print(paste("Threshold (u) :", sprintf("%.8f", threshold_u)))
## [1] "Threshold (u) : 0.01933154"
# 4. Ambil Data Exceedances & Hitung Excess
exceedances <- loss_sorted[1:jumlah_ekstrem]
excess_vals <- exceedances - threshold_u
PeakOverThreshold <- data.frame(
LossValue = exceedances,
Excess = sprintf("%.8f", excess_vals)
)
head(PeakOverThreshold)
## LossValue Excess
## 1 0.11779902 0.09846748
## 2 0.10625025 0.08691871
## 3 0.08390735 0.06457581
## 4 0.08061009 0.06127855
## 5 0.07176694 0.05243540
## 6 0.06989018 0.05055864
tail(PeakOverThreshold)
## LossValue Excess
## 142 0.02002187 0.00069033
## 143 0.01998837 0.00065683
## 144 0.01997622 0.00064468
## 145 0.01983171 0.00050017
## 146 0.01944838 0.00011684
## 147 0.01933154 0.00000000
View(PeakOverThreshold)
# Mean Residual Life Plot
evmix::mrlplot(port_loss,
main = "Mean Residual Life Plot",
xlab = "Threshold u",
ylab = "Mean Excess",
legend.loc = NULL )
legend("topright",
legend = c("Sample Mean Excess", "95% CI", "Threshold Model"),
col = c("black", "black", "blue"),
lty = c(1, 2, 1),
cex = 0.65,
bg = "white",
box.col = "gray")
# 8. GENERALIZED EXTREME VALUE --------------------------------------------
gevfit <- fevd(BlockMaxima$Max_Loss, type = "GEV", method = "MLE")
summary(gevfit)
##
## fevd(x = BlockMaxima$Max_Loss, type = "GEV", method = "MLE")
##
## [1] "Estimation Method used: MLE"
##
##
## Negative Log-Likelihood Value: -272.4126
##
##
## Estimated parameters:
## location scale shape
## 0.02093909 0.01203624 0.15646202
##
## Standard Error Estimates:
## location scale shape
## 0.001377596 0.001053116 0.083253049
##
## Estimated parameter covariance matrix.
## location scale shape
## location 1.897772e-06 7.821018e-07 -3.802290e-05
## scale 7.821018e-07 1.109054e-06 -1.233161e-05
## shape -3.802290e-05 -1.233161e-05 6.931070e-03
##
## AIC = -538.8252
##
## BIC = -531.0399
# 1. Plot Density
plot(gevfit, type = "density", main = "Density Plot - Generalized Extreme Value")
# 2. QQ-Plot
plot(gevfit, type = "qq", main = "QQ-Plot - Generalized Extreme Value")
# 9. GENERALIZED PARETO DISTRIBUTION --------------------------------------
gpdfit<- extRemes::fevd(ReturnPortofolio$Loss,
threshold = threshold_u,
type = "GP",
method = "MLE")
summary(gpdfit)
##
## extRemes::fevd(x = ReturnPortofolio$Loss, threshold = threshold_u,
## type = "GP", method = "MLE")
##
## [1] "Estimation Method used: MLE"
##
##
## Negative Log-Likelihood Value: -450.8467
##
##
## Estimated parameters:
## scale shape
## 0.01794833 -0.06775744
##
## Standard Error Estimates:
## scale shape
## 0.001838876 0.062369832
##
## Estimated parameter covariance matrix.
## scale shape
## scale 3.381465e-06 -7.694128e-05
## shape -7.694128e-05 3.889996e-03
##
## AIC = -897.6934
##
## BIC = -891.7262
# 1. Plot Density
plot(gpdfit, type = "density", main = "Density Plot - Generalized Pareto Distribution")
# 2. QQ-Plot
plot(gpdfit, type = "qq", main = "QQ-Plot - Generalized Pareto Distribution")
# 10. UJI KESESUAIAN DISTRIBUSI MENGGUNAKAN ANDERSON DARLING -------------------------------------------
# Generalized Extreme Value
par_gev <- distill(gevfit)
vec_gev <- c(par_gev["location"], par_gev["scale"], par_gev["shape"])
test_gev_gnfit <- gnFit::gnfit(dat = BlockMaxima$Max_Loss,
dist = "gev",
pr = vec_gev)
## Test of Hypothesis for gev distribution
## Cramer-von Misses Statistics: 0.1295 P-Value: 0.04468
## Anderson-Darling Statistics: 0.6946 P-Value: 0.06975
print(test_gev_gnfit)
## $Wpval
## [1] 0.04468385
##
## $Apval
## [1] 0.06975282
##
## $Cram
## [1] 0.1295
##
## $Ander
## [1] 0.6946
##
## attr(,"class")
## [1] "gnfit"
# Generalized Pareto Distribution
par_gpd <- distill(gpdfit)
vec_gpd <- c(par_gpd["scale"], par_gpd["shape"])
adtestgpd<- gnFit::gnfit(dat = ReturnPortofolio$Loss,
dist = "gpd",
pr = vec_gpd,
threshold = threshold_u)
## Test of Hypothesis for gpd distribution
## Cramer-von Misses Statistics: 0.0779 P-Value: 0.22067
## Anderson-Darling Statistics: 0.486 P-Value: 0.22586
print(adtestgpd)
## $Wpval
## [1] 0.2206736
##
## $Apval
## [1] 0.225859
##
## $Cram
## [1] 0.0779
##
## $Ander
## [1] 0.486
##
## attr(,"class")
## [1] "gnfit"
# 11. ESTIMASI VALUE AT RISK ----------------------------------------------
#VAR GEV
conf_level <- 0.95
p_gev <- conf_level
parametergev <- distill(gevfit)
mu_gev <- parametergev["location"]
sigma_gev <- parametergev["scale"]
xi_gev <- parametergev["shape"]
term_gev <- (-log(p_gev))^(-xi_gev)
VaR_GEV <- mu_gev - (sigma_gev / xi_gev) * (1 - term_gev)
cat("Value at Risk (VaR) GEV dengan tingkat kepercayaan", conf_level*100, "% adalah:", VaR_GEV, "\n")
## Value at Risk (VaR) GEV dengan tingkat kepercayaan 95 % adalah: 0.06644735
# VAR GPD
conf_level <- 0.95
p <- 1 - conf_level
parametergpd <- distill(gpdfit)
sigma <- parametergpd["scale"]
xi <- parametergpd["shape"]
u <- threshold_u
Nu <- sum(ReturnPortofolio$Loss > u)
n <- length(ReturnPortofolio$Loss)
VaR_GPD <- u + (sigma / xi) * (((n / Nu) * p)^(-xi) - 1)
cat("Value at Risk (VaR) dengan tingkat kepercayaan", conf_level*100, "% adalah:", VaR_GPD, "\n")
## Value at Risk (VaR) dengan tingkat kepercayaan 95 % adalah: 0.03132126
# 12. BACKTESTING ----------------------------------------------
Actual_Loss <- ReturnPortofolio$Loss
Actual_Loss
## [1] 0.000000e+00 7.757336e-03 6.482799e-03 1.539205e-02 -5.221693e-03
## [6] 8.208329e-03 1.015411e-02 1.071251e-03 8.989056e-03 1.636811e-02
## [11] 1.266640e-02 1.356593e-02 1.293229e-02 -1.102023e-02 -4.204237e-03
## [16] -1.302763e-03 -1.971755e-02 -8.291292e-03 -2.044347e-02 1.835341e-02
## [21] -1.314045e-02 0.000000e+00 -1.176312e-02 0.000000e+00 0.000000e+00
## [26] 0.000000e+00 0.000000e+00 0.000000e+00 -1.588879e-02 3.708730e-03
## [31] 6.946690e-03 6.998631e-03 1.651268e-04 6.609593e-03 -7.602398e-03
## [36] -1.527531e-02 1.445361e-03 3.267492e-03 1.412419e-03 -5.960920e-03
## [41] 1.026848e-02 -4.022827e-03 -8.125747e-03 -1.914126e-03 -4.424630e-04
## [46] 4.131811e-04 2.930607e-04 1.055939e-02 -6.671869e-03 -6.368714e-04
## [51] 1.908651e-03 -3.495570e-03 -9.976947e-04 -1.415084e-02 -1.145561e-02
## [56] 1.049843e-02 5.915571e-03 1.546020e-03 4.260693e-03 4.850584e-03
## [61] 1.871104e-03 -3.074782e-03 3.686837e-03 3.580679e-03 -5.391226e-03
## [66] -4.661456e-03 1.286659e-02 6.441569e-03 2.843356e-02 1.734846e-02
## [71] -1.096169e-02 -8.235899e-03 -3.572288e-04 2.785230e-03 8.605687e-03
## [76] -4.232512e-03 1.151178e-02 -2.474092e-03 2.238978e-03 5.421989e-03
## [81] 1.073394e-02 6.710874e-03 -7.254303e-03 1.267970e-02 2.113032e-03
## [86] 8.215297e-03 1.224924e-02 -1.251690e-02 3.359219e-02 1.341719e-02
## [91] 2.549376e-03 -3.162283e-02 -1.247500e-03 1.160886e-02 -2.428948e-02
## [96] -7.184111e-03 2.203913e-03 1.090177e-02 3.087392e-02 -9.201416e-03
## [101] -2.908385e-02 1.080845e-02 2.149866e-03 7.506699e-03 1.099348e-02
## [106] 6.859135e-03 -8.548081e-03 9.291842e-03 6.945015e-03 1.686791e-04
## [111] 3.803213e-02 -1.829679e-03 -1.611346e-02 1.790494e-02 -1.662985e-02
## [116] 9.673751e-03 7.849430e-03 -6.140184e-03 1.745900e-03 -8.587186e-04
## [121] -7.166954e-03 -6.788930e-03 -1.705167e-02 1.174611e-02 -6.868533e-04
## [126] -8.581865e-03 -2.460576e-02 1.573230e-02 4.967752e-03 -2.671601e-03
## [131] 2.366657e-03 8.266281e-03 3.682244e-03 2.451392e-03 -1.787598e-02
## [136] 1.799598e-02 3.742165e-03 2.316163e-03 8.938365e-03 1.132092e-03
## [141] 6.446664e-03 6.327794e-03 -5.145723e-03 -6.630547e-03 -6.157066e-03
## [146] 1.691475e-03 1.690677e-03 1.615374e-02 1.480588e-02 1.696014e-02
## [151] 2.573424e-02 2.995218e-02 -2.322486e-02 -1.400942e-02 -3.107015e-02
## [156] 2.075093e-03 1.221901e-02 -1.411171e-03 -2.187390e-03 6.950230e-04
## [161] 1.123875e-02 4.134660e-03 -4.097793e-03 -1.131008e-03 -4.298727e-03
## [166] -4.476488e-02 6.364657e-03 -1.512513e-02 1.610199e-03 4.237368e-03
## [171] 6.028499e-03 9.043554e-03 -4.550655e-03 3.088447e-03 1.296893e-02
## [176] 8.385250e-03 1.436667e-02 -1.774608e-02 5.341259e-03 -1.253568e-02
## [181] -5.840865e-03 4.118757e-03 2.123518e-03 -3.918022e-03 -4.772388e-03
## [186] 3.792373e-03 1.975770e-03 8.716616e-03 -6.101790e-03 1.096335e-02
## [191] -4.777217e-03 -9.149138e-03 1.539591e-02 1.881039e-02 8.951195e-03
## [196] -1.525021e-02 -1.109389e-02 -5.501339e-03 -1.293242e-02 1.272333e-02
## [201] -1.146962e-03 4.572720e-03 6.341083e-03 9.297761e-03 -3.231419e-03
## [206] 2.653147e-03 -5.581110e-03 -1.692430e-03 1.035806e-02 2.644272e-02
## [211] 1.624319e-02 3.282515e-02 3.966945e-02 5.576687e-02 5.207168e-02
## [216] -3.094393e-03 -2.406132e-02 -1.036826e-01 2.994007e-02 1.177990e-01
## [221] -9.115583e-02 3.215092e-02 8.061009e-02 2.915679e-03 4.168877e-02
## [226] 8.390735e-02 5.681254e-02 7.176694e-02 3.661337e-02 6.827908e-02
## [231] 5.659316e-02 -1.638236e-01 -1.432458e-01 5.016398e-02 -2.555057e-02
## [236] 3.707796e-02 -1.313195e-02 -2.575534e-02 -4.860739e-02 9.080577e-03
## [241] 5.262649e-02 1.712535e-03 -5.070718e-03 -1.680662e-02 2.514537e-02
## [246] 3.270306e-02 -4.442459e-02 1.983171e-02 1.755847e-02 -1.558985e-02
## [251] 2.426644e-03 3.883612e-02 -9.514231e-03 1.741055e-02 4.789707e-03
## [256] -5.432250e-02 -2.005464e-03 -1.027604e-01 -6.504487e-03 1.865075e-02
## [261] -4.331906e-03 5.186822e-02 -8.519427e-02 4.929852e-02 4.098217e-02
## [266] -2.944975e-02 -4.428513e-02 -1.942424e-02 -1.421633e-02 -3.399518e-02
## [271] -1.451607e-02 -1.268122e-02 -5.308582e-02 -2.105996e-02 1.506690e-02
## [276] -1.489734e-02 -4.502674e-02 2.563106e-02 4.238613e-02 3.069366e-02
## [281] -4.091577e-02 3.560682e-02 -5.781835e-02 7.626569e-03 1.263048e-02
## [286] -3.707805e-03 1.755055e-02 4.427767e-03 -3.638628e-02 1.439242e-02
## [291] 7.257372e-03 3.860663e-03 -3.542373e-03 -2.276283e-03 -2.978437e-03
## [296] -1.747437e-02 -1.085828e-01 -6.277517e-02 -9.564745e-03 8.487200e-03
## [301] -3.573435e-02 -1.266078e-02 -1.027652e-02 3.910003e-03 -3.044809e-03
## [306] 1.091633e-02 1.929640e-02 -2.404129e-02 2.298768e-03 -2.517088e-02
## [311] 1.874415e-02 -7.595027e-03 -9.919796e-02 4.112001e-02 9.376484e-04
## [316] 4.371750e-02 -2.770222e-02 -1.776252e-02 -9.473124e-03 5.921982e-03
## [321] -7.638090e-03 -1.937552e-02 -3.344298e-02 7.151450e-03 -1.692730e-03
## [326] -2.536248e-02 9.177062e-04 -8.869386e-02 -9.230021e-03 -8.759456e-02
## [331] -4.826776e-02 -1.670270e-03 2.172567e-02 -2.090548e-02 4.009694e-03
## [336] 1.017845e-02 -7.684646e-03 1.330094e-02 -6.543530e-04 4.007649e-02
## [341] 6.989018e-02 -1.635611e-02 -5.379629e-02 2.335791e-02 2.070930e-02
## [346] 1.708662e-02 -5.440360e-03 3.197402e-02 4.626172e-02 1.753085e-02
## [351] 2.540317e-02 -5.144048e-02 2.258675e-02 1.481261e-02 1.285726e-03
## [356] -4.706754e-02 1.708655e-02 -4.733375e-02 -1.505288e-02 -3.377373e-03
## [361] -4.136190e-03 -7.773138e-05 -3.095303e-02 -1.115989e-01 -1.146235e-01
## [366] 4.572538e-02 -2.627992e-02 -1.181298e-02 -2.630621e-02 3.880995e-02
## [371] 3.324692e-02 3.200996e-02 -2.581064e-02 6.887234e-03 2.727638e-03
## [376] 8.962568e-03 1.926922e-02 -6.446434e-02 3.099631e-03 -4.508699e-03
## [381] -2.769995e-02 -2.360951e-02 1.506913e-02 -1.465458e-02 1.892227e-03
## [386] -7.613601e-03 -2.168465e-02 -2.423145e-03 9.421701e-03 -1.018384e-02
## [391] -5.524691e-03 -1.168766e-02 -8.566029e-03 -2.687462e-02 3.523184e-02
## [396] -2.552163e-02 -7.448834e-03 -1.066854e-02 1.040518e-02 -1.456546e-02
## [401] 6.310420e-03 -1.341645e-02 -8.734379e-02 -9.105942e-02 1.535057e-02
## [406] -1.299461e-02 -4.808983e-03 -2.460231e-02 -2.253215e-02 3.397787e-02
## [411] 1.100580e-02 -1.056376e-02 2.264764e-03 1.238103e-02 -3.485611e-02
## [416] -2.005043e-03 -2.482507e-02 -4.069692e-02 -3.317275e-02 -5.150346e-02
## [421] -1.005051e-01 -1.633197e-03 6.765525e-03 2.237850e-02 2.316922e-02
## [426] 3.285234e-02 -8.246409e-02 2.869887e-02 3.795975e-02 -2.557228e-03
## [431] 4.135130e-02 3.836478e-02 4.248932e-02 6.012747e-02 -7.902423e-02
## [436] 4.067194e-02 -2.994874e-02 6.531777e-03 -5.725978e-03 -4.231052e-02
## [441] 1.816738e-02 -5.748962e-03 2.086487e-04 1.021677e-03 -7.682002e-03
## [446] 3.407985e-02 1.399545e-02 -7.018880e-03 -1.235123e-02 -3.066082e-03
## [451] -3.478595e-03 -1.954181e-02 8.319363e-03 -2.266839e-02 1.290169e-02
## [456] 6.832334e-03 3.330899e-02 8.725625e-03 -4.442214e-03 1.782845e-02
## [461] 2.468225e-03 -1.635341e-02 7.069662e-03 -1.368926e-02 -1.033004e-04
## [466] -1.723011e-02 1.140440e-02 1.808262e-02 4.461081e-03 3.577844e-03
## [471] 2.478981e-02 -1.521837e-02 1.997622e-02 2.819066e-02 2.565854e-02
## [476] -6.408629e-03 2.389517e-02 -1.163060e-02 8.491283e-04 -4.313092e-02
## [481] 2.540657e-03 3.644854e-02 3.743938e-03 -2.790105e-02 5.222433e-03
## [486] -3.829278e-03 -2.385707e-02 1.888095e-02 1.576714e-02 3.697743e-04
## [491] -3.775356e-03 1.379250e-02 -3.810966e-03 1.435043e-02 -1.292944e-02
## [496] 2.241407e-03 1.484332e-02 -5.843349e-03 -6.786830e-03 -2.977666e-02
## [501] 2.917069e-02 5.114930e-03 9.255601e-03 3.437475e-02 2.489440e-02
## [506] 3.653136e-02 -5.398017e-03 1.147935e-02 2.380583e-02 -2.995145e-02
## [511] 1.719831e-02 -1.786381e-02 -2.338810e-02 -1.174946e-02 -1.137160e-02
## [516] -2.513135e-02 3.702271e-02 3.063532e-02 -1.762834e-02 -1.162973e-02
## [521] 1.377825e-02 7.238186e-03 4.541840e-03 1.560971e-02 -1.527432e-02
## [526] 3.045624e-02 1.687247e-02 -3.255861e-02 2.753738e-02 7.654127e-03
## [531] -5.332492e-02 -5.507481e-02 1.163148e-02 -2.832704e-02 1.071359e-03
## [536] 6.212223e-03 2.185928e-02 -3.872892e-05 -2.898481e-02 -2.507214e-02
## [541] 1.712528e-02 -3.734457e-04 1.822651e-02 -5.020898e-03 -2.181901e-02
## [546] -1.157598e-02 -1.952654e-02 -4.057283e-03 -1.478850e-02 -3.543129e-03
## [551] 6.735394e-04 -4.839952e-03 -1.414661e-02 -1.385358e-03 4.013420e-02
## [556] 5.111860e-03 9.478549e-04 -1.249749e-02 -4.106991e-02 1.229687e-02
## [561] 4.105606e-02 3.130397e-02 -6.439774e-03 -1.143143e-02 2.271212e-02
## [566] 3.203288e-03 3.777215e-02 -2.453762e-02 -1.314611e-02 1.111200e-02
## [571] -7.471850e-03 7.939809e-03 8.853295e-03 -2.101677e-02 -5.970225e-03
## [576] 1.318467e-02 9.257155e-03 -7.587687e-03 3.163868e-03 1.710002e-03
## [581] 7.306944e-03 -1.201982e-04 -7.889549e-03 -5.334808e-03 3.976724e-03
## [586] 9.116219e-03 -1.288538e-02 3.231510e-03 1.685431e-02 7.222012e-03
## [591] -1.540130e-02 -1.238828e-02 8.214066e-03 1.400020e-02 3.558091e-03
## [596] -8.612802e-04 -2.009221e-02 6.132317e-03 -3.946678e-02 1.203602e-02
## [601] -4.552458e-02 1.103838e-02 -1.329758e-02 1.161568e-02 -3.045582e-03
## [606] -1.118184e-02 -9.876811e-03 -7.174957e-03 -2.865579e-02 7.640973e-03
## [611] 1.638356e-02 -7.677998e-03 1.202258e-02 -6.590447e-03 7.672035e-03
## [616] 2.002187e-02 -1.286503e-02 7.912721e-03 1.168562e-02 -1.224877e-02
## [621] 6.312209e-03 -3.743108e-03 -2.976222e-03 2.726696e-03 -6.765866e-03
## [626] 1.797199e-04 1.063430e-02 2.056781e-03 -8.117758e-03 -3.552125e-03
## [631] 8.685934e-03 -6.089481e-03 -2.426689e-03 1.059727e-02 -5.404360e-04
## [636] -4.876811e-03 2.304930e-02 5.036179e-03 1.331043e-02 2.375185e-02
## [641] -1.063979e-03 -1.092193e-02 -4.766884e-04 -4.331611e-03 -8.442805e-03
## [646] 1.204651e-03 4.065770e-03 4.710002e-03 3.187081e-03 -2.051390e-03
## [651] 1.027511e-02 7.661899e-04 1.381104e-02 3.420661e-03 1.053937e-02
## [656] -3.087842e-03 -5.664843e-03 -1.659851e-02 1.370066e-02 2.630542e-03
## [661] 3.503173e-03 -3.109422e-03 -1.054891e-02 3.098676e-03 1.293655e-02
## [666] -6.399481e-03 -2.454799e-03 4.227153e-03 3.078252e-02 1.403336e-03
## [671] 4.044377e-03 1.361515e-02 1.591444e-02 4.172347e-03 -2.037118e-02
## [676] -9.844901e-03 7.424410e-03 1.786376e-02 -9.066324e-03 -2.913983e-03
## [681] -8.610960e-03 3.118353e-03 -4.237942e-03 -1.171075e-02 -1.022364e-03
## [686] -2.708751e-02 -7.608743e-03 -1.115367e-02 3.390024e-03 -1.269219e-03
## [691] 1.795666e-02 -1.833824e-02 -2.323749e-03 6.804702e-03 -1.885889e-02
## [696] -1.677606e-02 1.128017e-02 -7.100850e-03 4.084553e-02 -2.099687e-02
## [701] -3.604950e-02 1.033635e-02 6.729273e-03 2.712515e-02 1.433791e-02
## [706] -2.252287e-02 -5.614686e-03 7.234463e-03 -1.351127e-02 1.226142e-03
## [711] -5.007549e-03 7.869796e-03 1.283692e-02 -9.240258e-04 -6.521419e-03
## [716] 5.181365e-04 -7.968803e-03 4.640786e-03 -5.759558e-03 1.725243e-03
## [721] -1.526645e-03 3.878628e-03 1.427690e-04 7.042582e-03 4.802524e-03
## [726] 2.926798e-02 -6.990417e-03 -2.428517e-03 7.675980e-03 -3.311917e-04
## [731] -7.408712e-04 -1.142119e-02 -1.562890e-02 1.436348e-02 -1.163462e-02
## [736] -1.867965e-02 1.069722e-02 3.073806e-03 -1.466622e-02 4.217342e-03
## [741] -2.831670e-02 5.406599e-02 6.264468e-03 2.797626e-03 5.364263e-02
## [746] -6.062057e-03 -1.303318e-02 -6.935982e-03 1.349631e-02 -9.731776e-03
## [751] 1.409808e-02 -7.128297e-03 6.716537e-03 -3.188417e-02 8.936760e-03
## [756] -1.736992e-02 1.304328e-02 -1.510164e-02 8.867222e-03 7.279573e-03
## [761] -1.583867e-02 4.674247e-03 1.693402e-02 1.192419e-02 -2.444472e-03
## [766] -2.957818e-03 -8.362267e-03 1.889049e-02 -3.862056e-03 -3.699443e-03
## [771] 1.084380e-02 3.142135e-03 -3.026868e-03 1.206623e-02 4.416344e-03
## [776] 1.007941e-02 6.681791e-03 2.776173e-02 4.437968e-02 -1.301483e-02
## [781] 8.204764e-04 -1.241682e-03 -1.447481e-02 3.622716e-03 -9.001716e-02
## [786] 4.488645e-02 -2.931532e-03 -9.586489e-03 -2.839092e-02 -1.386504e-03
## [791] -2.932193e-02 -6.760236e-03 4.208286e-03 -8.487518e-03 -2.118459e-02
## [796] 1.138566e-03 -1.671041e-02 6.255802e-03 2.620322e-03 1.201852e-02
## [801] -3.493460e-03 -8.538964e-03 -3.202211e-03 5.026119e-03 5.084628e-04
## [806] 1.519720e-03 -1.004557e-02 3.967660e-03 6.504284e-03 4.440033e-03
## [811] -8.626651e-03 -1.354195e-02 9.805760e-03 5.245943e-03 5.349212e-03
## [816] 6.560815e-04 1.499278e-03 -4.611528e-03 3.439635e-04 -7.560660e-03
## [821] -1.888105e-03 4.009392e-04 -6.169369e-03 2.370365e-03 3.789048e-03
## [826] -7.541679e-03 2.882488e-03 9.322231e-04 -6.750790e-03 5.457383e-03
## [831] -2.883919e-02 1.358942e-02 -5.433214e-03 3.098274e-03 3.073254e-03
## [836] -3.593258e-03 -9.521111e-03 8.948768e-04 3.918696e-03 5.333808e-03
## [841] 1.052442e-02 3.902227e-03 -6.291359e-03 4.984019e-04 3.695977e-03
## [846] 5.328188e-05 1.495660e-02 7.327791e-03 9.590951e-03 1.071031e-02
## [851] 1.132451e-02 1.863486e-02 2.733891e-03 -9.555647e-03 5.561981e-03
## [856] -1.641248e-02 -2.831579e-02 -2.424609e-02 1.519113e-03 1.296051e-02
## [861] -7.258221e-03 -6.758847e-03 -9.751226e-03 6.591732e-04 2.206175e-03
## [866] 7.664325e-03 -6.266621e-04 -8.879495e-04 9.140314e-03 -3.497867e-03
## [871] 5.687272e-03 -1.007416e-02 6.272131e-03 6.013161e-04 1.538565e-02
## [876] -5.600020e-03 -3.211930e-03 2.229020e-03 -4.270288e-03 -9.883471e-03
## [881] -5.995690e-03 5.613720e-03 1.760733e-03 6.644885e-03 -1.736995e-02
## [886] 1.338166e-02 1.843520e-03 6.562840e-05 8.802015e-03 2.553638e-02
## [891] 4.617134e-03 1.480150e-02 -9.811881e-03 -2.136721e-02 1.933154e-02
## [896] 7.371120e-03 -5.162895e-03 3.569833e-02 1.046392e-02 -2.108217e-02
## [901] -2.720770e-02 6.437337e-03 -4.066628e-02 1.392053e-02 3.932364e-03
## [906] -7.162927e-03 -3.275508e-04 4.502394e-03 -4.002635e-02 8.680056e-03
## [911] 2.749554e-02 -1.858703e-02 7.146893e-03 3.276843e-02 6.704727e-03
## [916] -8.192256e-03 6.815533e-03 -9.823377e-03 -2.125526e-02 3.509949e-03
## [921] -1.465332e-03 -2.075392e-02 7.012975e-03 5.698380e-03 -2.622327e-02
## [926] 2.160947e-04 6.923539e-03 2.180939e-02 -1.901917e-03 1.033068e-03
## [931] -1.722824e-02 1.633996e-02 -1.365482e-02 -3.300728e-03 3.892797e-03
## [936] -4.151437e-03 -1.427770e-02 -1.197541e-02 -6.531367e-02 3.255616e-04
## [941] -2.807377e-02 3.407953e-03 5.777153e-03 3.991902e-02 -1.573661e-02
## [946] -6.343121e-05 2.909401e-02 7.813296e-03 -2.394605e-02 5.131387e-03
## [951] 7.387052e-03 -8.864308e-04 -1.223683e-02 7.354637e-03 -1.588629e-02
## [956] 1.326286e-02 -6.206512e-03 3.645727e-02 -3.724482e-03 -1.578058e-02
## [961] -2.559462e-02 2.120355e-02 -1.718713e-02 -2.692591e-02 6.904725e-03
## [966] -4.316392e-03 -3.175108e-02 1.944838e-02 -1.119920e-02 -1.047582e-02
## [971] 9.189934e-03 -2.215869e-02 -1.521893e-02 2.758890e-03 5.341784e-03
## [976] -3.008337e-03 1.393509e-02 -2.495832e-02 1.828767e-02 -1.443916e-03
## [981] 2.237272e-03 6.733368e-03 -1.093457e-02 7.992658e-03 -3.504956e-03
## [986] -9.492961e-03 -1.493446e-03 3.928819e-03 5.013397e-03 -1.392686e-02
## [991] 1.198097e-02 -9.672671e-03 2.338220e-02 3.756258e-02 -1.837437e-03
## [996] -4.357214e-02 -1.844928e-03 5.939979e-03 -6.376303e-04 -7.868436e-03
## [1001] -1.223840e-02 -8.468320e-03 6.133558e-03 5.736544e-03 -1.472065e-03
## [1006] 1.119838e-02 -9.233175e-04 4.538376e-03 -7.295296e-04 4.349823e-03
## [1011] -9.613765e-04 1.204949e-03 -5.188404e-03 1.807198e-03 7.951248e-03
## [1016] 6.853573e-04 -6.637898e-04 -9.412339e-03 4.634865e-03 3.003592e-04
## [1021] -1.069003e-02 -5.304501e-03 -2.204765e-02 9.553521e-03 1.044933e-02
## [1026] 5.801727e-04 3.703702e-03 -3.155107e-03 -1.095976e-02 9.128599e-03
## [1031] -2.127507e-03 4.276912e-03 3.336339e-03 -8.127122e-03 -5.042374e-03
## [1036] 3.273576e-03 3.378824e-03 -4.644840e-03 2.929446e-03 1.382510e-03
## [1041] -1.152902e-03 5.350506e-03 7.486047e-03 -3.048537e-03 2.130041e-03
## [1046] -2.406497e-02 1.242977e-03 -7.568480e-03 1.816758e-03 6.904259e-03
## [1051] -1.177803e-02 -3.345385e-03 6.620763e-03 -4.956305e-04 3.838683e-03
## [1056] 7.212007e-04 -1.551506e-03 9.904999e-04 -2.218868e-03 -3.374049e-03
## [1061] 2.021669e-03 1.537259e-03 -8.436206e-03 3.983533e-03 8.954554e-04
## [1066] 6.208657e-03 -4.101757e-05 1.378717e-02 3.098572e-03 -7.185210e-03
## [1071] 8.267189e-03 -3.899512e-03 -2.223424e-03 1.219722e-03 1.710611e-02
## [1076] -1.057057e-02 -3.131497e-02 2.145840e-02 3.033749e-03 6.842093e-03
## [1081] 1.035828e-02 -5.130992e-03 -3.702077e-03 -3.085572e-03 1.821697e-02
## [1086] 8.642417e-03 -6.740442e-03 5.359370e-03 -5.909691e-04 -4.361932e-03
## [1091] 8.069584e-06 -1.478949e-02 1.518613e-02 6.002830e-03 1.326427e-03
## [1096] 8.816618e-03 1.913391e-02 -9.797035e-03 1.524609e-02 -2.061045e-02
## [1101] -3.972571e-04 1.787297e-02 -5.829370e-03 2.497869e-03 8.305640e-03
## [1106] 9.866093e-03 -2.072155e-02 -2.838437e-03 -1.385883e-02 8.378635e-03
## [1111] 1.267786e-02 -3.202496e-03 1.269016e-02 -2.394431e-05 -8.509832e-03
## [1116] -2.792976e-02 -3.240359e-03 -1.698618e-02 -4.751765e-03 7.099261e-04
## [1121] 3.576828e-03 -7.128496e-03 -9.511611e-03 3.469382e-03 -3.325855e-03
## [1126] 6.024375e-03 -4.213518e-03 -8.242068e-03 -1.427106e-02 -1.800029e-03
## [1131] 1.789422e-03 1.468956e-02 7.268332e-03 2.578354e-03 7.230492e-03
## [1136] 2.969911e-03 -3.855966e-02 3.577839e-04 2.921401e-03 -6.351176e-03
## [1141] -1.307443e-02 1.581233e-02 -4.546187e-03 -8.376025e-04 -1.948524e-02
## [1146] 2.008411e-03 -3.434901e-03 -1.206823e-02 -3.841960e-02 -6.028187e-03
## [1151] -2.791039e-03 -1.100529e-02 6.445485e-03 -1.070825e-02 -1.022605e-02
## [1156] 1.038779e-02 3.632456e-03 -4.253392e-03 -1.248915e-02 2.897596e-04
## [1161] -1.747608e-02 -1.262324e-02 2.492636e-02 1.438808e-02 1.456166e-02
## [1166] -4.654848e-02 -1.718036e-02 -3.221752e-02 5.374493e-03 -1.009041e-02
## [1171] 2.017487e-03 -2.833276e-03 -1.441133e-02 -1.298755e-02 8.415520e-03
## [1176] -1.825048e-02 9.803540e-03 -5.416648e-03 -2.728821e-02 6.234462e-03
## [1181] 3.072030e-03 6.983354e-03 3.323196e-03 -1.714326e-02 4.828785e-04
## [1186] 9.062619e-03 1.075333e-02 4.995523e-03 -6.510303e-03 -1.354137e-02
## [1191] -6.250581e-03 -2.690891e-02 -4.668323e-02 1.616259e-02 1.410296e-02
## [1196] 1.046399e-02 -6.951395e-03 -4.754755e-03 -2.893997e-03 8.403041e-03
## [1201] -1.706366e-02 -2.411893e-03 -6.251277e-03 4.037617e-03 4.644121e-02
## [1206] -1.930282e-02 2.132654e-02 -2.614890e-02 8.548950e-03 4.632968e-02
## [1211] 1.293406e-02 -3.066385e-02 1.834198e-02 5.017025e-04 -1.952978e-02
## [1216] -1.579928e-02 1.829545e-02 3.789172e-02 -1.456416e-02 -2.776346e-02
## [1221] 4.732858e-02 -1.641816e-02 -3.156067e-02 2.155338e-02 3.482407e-02
## [1226] 4.526643e-02 -1.349464e-02 -4.424233e-02 -3.322589e-03 -7.021418e-03
## [1231] 2.591428e-02 3.802377e-02 3.454710e-03 2.699474e-02 -7.914701e-03
## [1236] 3.167630e-02 6.456585e-03 -1.201139e-02 -2.065819e-02 -1.140604e-02
## [1241] 8.553913e-03 4.724313e-03 6.869571e-03 6.925537e-03 2.831849e-03
## [1246] 1.164416e-02 -2.475375e-02 9.622920e-03 -2.094670e-02 -2.518148e-02
## [1251] -1.090157e-02 -1.242059e-02 5.412808e-03 -4.292343e-03 -1.150403e-02
## [1256] -2.688400e-02 -1.597925e-03 1.177906e-02 8.618637e-03 -1.400524e-03
## [1261] -7.347566e-03 1.331587e-02 -2.316971e-02 9.982464e-03 -8.162769e-03
## [1266] -3.804754e-03 1.026860e-02 8.307754e-03 -5.049339e-03 -1.392883e-02
## [1271] 7.439120e-03 -2.543528e-02 9.884726e-03 1.126904e-02 1.162603e-02
## [1276] -8.778576e-03 -1.248738e-03 4.867622e-03 -2.212541e-02 -1.084379e-02
## [1281] 7.894058e-03 4.262637e-02 -2.146643e-02 -9.835161e-03 -4.087748e-03
## [1286] -1.430152e-02 -4.253609e-03 -1.840256e-02 -2.024485e-03 8.598706e-04
## [1291] 3.729017e-03 -1.162944e-03 -1.192748e-02 -1.179472e-02 2.032670e-02
## [1296] -1.828754e-02 -9.431707e-03 5.083504e-03 -5.061608e-03 1.532094e-02
## [1301] 1.947252e-03 5.532101e-03 8.273387e-03 1.037564e-03 -1.580556e-02
## [1306] -2.738152e-03 2.726379e-03 -8.173036e-03 -1.968070e-02 -2.037009e-02
## [1311] 1.601762e-03 -4.331372e-02 -9.078358e-03 -9.625993e-03 2.556595e-02
## [1316] -2.810212e-02 8.473567e-03 1.722670e-02 4.899049e-03 1.032581e-02
## [1321] 2.096164e-02 -8.666933e-03 1.585730e-02 -5.675773e-03 1.382632e-02
## [1326] 7.081843e-03 -3.504569e-02 1.262016e-02 -4.191982e-03 5.288757e-03
## [1331] -1.867624e-03 -9.628874e-03 3.224294e-03 -2.467977e-02 1.271377e-03
## [1336] 3.365088e-03 2.048262e-02 -4.800705e-03 -7.596977e-03 1.071657e-02
## [1341] 9.941513e-03 1.458502e-02 3.343084e-03 -1.059793e-02 1.418343e-02
## [1346] -1.772319e-03 -1.221228e-02 2.779042e-02 1.865269e-02 4.159297e-03
## [1351] 7.905430e-03 -1.285726e-02 -5.525155e-03 1.112332e-02 6.755465e-04
## [1356] 7.435396e-03 1.516365e-02 7.062485e-04 2.275777e-02 -5.212115e-02
## [1361] -1.828231e-02 1.506659e-02 1.403077e-03 1.304240e-02 2.388712e-02
## [1366] -3.506814e-02 -1.734530e-02 1.436954e-02 -2.690222e-03 -1.738723e-02
## [1371] 8.322244e-03 -1.548817e-03 2.596805e-02 9.312636e-03 4.526574e-03
## [1376] 2.721009e-02 1.998837e-02 1.724577e-02 -1.738659e-02 -2.133220e-02
## [1381] 1.161968e-02 -6.700508e-03 1.296997e-02 -2.382379e-02 1.160206e-02
## [1386] 1.498120e-02 1.152299e-02 -2.028886e-03 -1.053189e-02 7.963886e-03
## [1391] 6.482637e-03 1.820235e-02 -4.261298e-02 2.545853e-03 -1.060942e-02
## [1396] -6.212329e-03 -2.150425e-02 2.653496e-03 -6.997018e-03 1.291167e-02
## [1401] 2.886270e-03 -1.575941e-02 9.405965e-03 -1.847235e-03 1.630426e-02
## [1406] 3.682041e-02 -3.334179e-02 7.695212e-03 1.342387e-02 -7.034224e-03
## [1411] 1.539520e-03 2.688907e-03 -3.389984e-02 -1.056990e-02 3.491888e-02
## [1416] 1.358939e-02 -1.073244e-02 -2.713489e-03 2.357790e-02 1.644147e-02
## [1421] 6.253670e-02 4.158302e-02 -6.194438e-02 2.174083e-02 -1.567112e-02
## [1426] -1.211579e-02 1.252160e-02 9.428657e-03 9.053319e-03 -1.881545e-02
## [1431] 9.147966e-03 1.083337e-02 7.622409e-03 3.002797e-02 -1.369517e-03
## [1436] 5.352320e-02 3.819875e-02 -6.228225e-03 -7.690389e-02 -4.153149e-02
## [1441] 9.328251e-03 1.062502e-01 -2.467139e-02 -4.985676e-02 -4.482582e-03
## [1446] -5.278178e-02 -3.244790e-03 1.247711e-02 -1.894326e-02 -1.660594e-02
## [1451] -1.422167e-02 -2.936857e-02 1.121201e-02 -1.207277e-02 -1.399203e-02
## [1456] 5.321332e-04 -5.891988e-04 -6.671886e-03 -6.819167e-03 -1.890332e-02
## [1461] 1.550137e-02 4.077983e-02 -9.660248e-03 -4.486620e-02 -1.804593e-02
## [1466] -2.763110e-05 -2.625496e-03 -1.259372e-03 -1.281125e-02 1.926753e-03
## [1471] -4.701550e-03 -3.033387e-03 1.862772e-03 -5.406388e-03
T_Total <- length(Actual_Loss)
T_Total
## [1] 1474
conf_level <- 0.95
p_expected <- 1 - conf_level
p_expected
## [1] 0.05
N_Expected <- ceiling(T_Total * p_expected)
N_Expected
## [1] 74
# HITUNG STATISTIK UNTUK GEV
# Hitung Failure Rate
Is_Violation_GEV <- ifelse(Actual_Loss > VaR_GEV, 1, 0)
N_Failures_GEV <- sum(Is_Violation_GEV)
Failure_Rate_GEV <- N_Failures_GEV / T_Total
# Hitung LR Kupiec GEV
term1_gev <- (p_expected ^ N_Failures_GEV) * ((1 - p_expected) ^ (T_Total - N_Failures_GEV))
term2_gev <- (Failure_Rate_GEV ^ N_Failures_GEV) * ((1 - Failure_Rate_GEV) ^ (T_Total - N_Failures_GEV))
LR_POF_GEV <- -2 * log(term1_gev / term2_gev)
# Hitung P-Value GEV
P_Value_GEV <- 1 - pchisq(LR_POF_GEV, df = 1)
# HITUNG STATISTIK UNTUK GPD
# Hitung Failure Rate
Is_Violation_GPD <- ifelse(Actual_Loss > VaR_GPD, 1, 0)
N_Failures_GPD <- sum(Is_Violation_GPD)
Failure_Rate_GPD <- N_Failures_GPD / T_Total
# Hitung LR Kupiec GPD
term1_gpd <- (p_expected ^ N_Failures_GPD) * ((1 - p_expected) ^ (T_Total - N_Failures_GPD))
term2_gpd <- (Failure_Rate_GPD ^ N_Failures_GPD) * ((1 - Failure_Rate_GPD) ^ (T_Total - N_Failures_GPD))
LR_POF_GPD <- -2 * log(term1_gpd / term2_gpd)
# Hitung P-Value GPD
P_Value_GPD <- 1 - pchisq(LR_POF_GPD, df = 1)
Tabel_Perbandingan <- tibble(
Indikator = c(
"Model VaR",
"Total Data",
"Target Pelanggaran",
"Jumlah Pelanggaran",
"Tingkat Pelanggaran",
"Selisih dari Target 5%",
"lLikelihood Ratio",
"P-Value"
),
`Hasil VAR-GEV` = c(
"Generalized Extreme Value",
as.character(T_Total),
paste0(p_expected * 100, "% (", N_Expected, " hari)"),
as.character(N_Failures_GEV),
paste0(sprintf("%.4f", Failure_Rate_GEV * 100), "%"),
paste0(sprintf("%.4f", abs(Failure_Rate_GEV - p_expected) * 100), "%"),
sprintf("%.4f", LR_POF_GEV),
sprintf("%.4f", P_Value_GEV)
),
`Hasil VAR-GPD` = c(
"Generalized Pareto Distribution",
as.character(T_Total),
paste0(p_expected * 100, "% (", N_Expected, " hari)"),
as.character(N_Failures_GPD),
paste0(sprintf("%.4f", Failure_Rate_GPD * 100), "%"),
paste0(sprintf("%.4f", abs(Failure_Rate_GPD - p_expected) * 100), "%"),
sprintf("%.4f", LR_POF_GPD),
sprintf("%.4f", P_Value_GPD)
)
)
print(Tabel_Perbandingan)
## # A tibble: 8 × 3
## Indikator `Hasil VAR-GEV` `Hasil VAR-GPD`
## <chr> <chr> <chr>
## 1 Model VaR Generalized Extreme Value Generalized Pareto Distribut…
## 2 Total Data 1474 1474
## 3 Target Pelanggaran 5% (74 hari) 5% (74 hari)
## 4 Jumlah Pelanggaran 7 81
## 5 Tingkat Pelanggaran 0.4749% 5.4953%
## 6 Selisih dari Target 5% 4.5251% 0.4953%
## 7 lLikelihood Ratio 103.5705 0.7384
## 8 P-Value 0.0000 0.3902
TabelBacktesting <- data.frame(
Hari_ke = index(ReturnPortofolio),
# Menampilkan Loss
DataLoss = as.numeric(ReturnPortofolio$Loss) * 100,
# Menampilkan VaR GEV
VaRGEV = rep(VaR_GEV * 100, length(ReturnPortofolio$Loss)),
# Status Pelanggaran GEV
LRGEV = ifelse(ReturnPortofolio$Loss > VaR_GEV,
"PELANGGARAN",
"TIDAK TERJADI PELANGGARAN"),
# Menampilkan VaR GPD
VaRGPD = rep(VaR_GPD * 100, length(ReturnPortofolio$Loss)),
# Status Pelanggaran GPD
LRGPD = ifelse(ReturnPortofolio$Loss > VaR_GPD,
"PELANGGARAN",
"TIDAK TERJADI PELANGGARAN")
)
head(TabelBacktesting)
## Hari_ke DataLoss VaRGEV LRGEV VaRGPD
## 1 1 0.0000000 6.644735 TIDAK TERJADI PELANGGARAN 3.132126
## 2 2 0.7757336 6.644735 TIDAK TERJADI PELANGGARAN 3.132126
## 3 3 0.6482799 6.644735 TIDAK TERJADI PELANGGARAN 3.132126
## 4 4 1.5392053 6.644735 TIDAK TERJADI PELANGGARAN 3.132126
## 5 5 -0.5221693 6.644735 TIDAK TERJADI PELANGGARAN 3.132126
## 6 6 0.8208329 6.644735 TIDAK TERJADI PELANGGARAN 3.132126
## LRGPD
## 1 TIDAK TERJADI PELANGGARAN
## 2 TIDAK TERJADI PELANGGARAN
## 3 TIDAK TERJADI PELANGGARAN
## 4 TIDAK TERJADI PELANGGARAN
## 5 TIDAK TERJADI PELANGGARAN
## 6 TIDAK TERJADI PELANGGARAN
tail(TabelBacktesting)
## Hari_ke DataLoss VaRGEV LRGEV VaRGPD
## 1469 1469 -1.2811253 6.644735 TIDAK TERJADI PELANGGARAN 3.132126
## 1470 1470 0.1926753 6.644735 TIDAK TERJADI PELANGGARAN 3.132126
## 1471 1471 -0.4701550 6.644735 TIDAK TERJADI PELANGGARAN 3.132126
## 1472 1472 -0.3033387 6.644735 TIDAK TERJADI PELANGGARAN 3.132126
## 1473 1473 0.1862772 6.644735 TIDAK TERJADI PELANGGARAN 3.132126
## 1474 1474 -0.5406388 6.644735 TIDAK TERJADI PELANGGARAN 3.132126
## LRGPD
## 1469 TIDAK TERJADI PELANGGARAN
## 1470 TIDAK TERJADI PELANGGARAN
## 1471 TIDAK TERJADI PELANGGARAN
## 1472 TIDAK TERJADI PELANGGARAN
## 1473 TIDAK TERJADI PELANGGARAN
## 1474 TIDAK TERJADI PELANGGARAN
View(TabelBacktesting, title = "Hasil Backtesting Lengkap")