This function plots colored bands for time series percentiles and confidence
intervals. You can use it for outputs from simdiff,
esgmartingaletest, esgcortest.
esgplotbands(x, ...)Arguments
- x
a times series object
- ...
additionnal (optional) parameters provided to
plot
See also
Examples
# Times series
kappa <- 1.5
V0 <- theta <- 0.04
sigma <- 0.2
theta1 <- kappa*theta
theta2 <- kappa
theta3 <- sigma
x <- simdiff(n = 100, horizon = 5,
frequency = "quart",
model = "OU",
x0 = V0, theta1 = theta1, theta2 = theta2, theta3 = theta3)
#par(mfrow=c(2,1))
esgplotbands(x, xlab = "time", ylab = "values")
matplot(as.vector(time(x)), x, type = 'l', xlab = "time", ylab = "series values")
# Martingale test
r0 <- 0.03
S0 <- 100
sigma0 <- 0.1
nbScenarios <- 100
horizon0 <- 10
eps0 <- simshocks(n = nbScenarios, horizon = horizon0, frequency = "quart",
method = "anti")
sim.GBM <- simdiff(n = nbScenarios, horizon = horizon0, frequency = "quart",
model = "GBM",
x0 = S0, theta1 = r0, theta2 = sigma0,
eps = eps0)
mc.test <- esgmartingaletest(r = r0, X = sim.GBM, p0 = S0, alpha = 0.05)
#>
#> martingale '1=1' one Sample t-test
#>
#> alternative hypothesis: true mean of the martingale difference is not equal to 0
#>
#> df = 99
#> t p-value
#> 0 Q2 -0.02247605 0.9821135
#> 0 Q3 0.01097937 0.9912620
#> 0 Q4 -0.15143897 0.8799376
#> 1 Q1 -0.13883348 0.8898638
#> 1 Q2 -0.19789551 0.8435326
#> 1 Q3 -0.22536473 0.8221601
#> 1 Q4 -0.26997124 0.7877443
#> 2 Q1 -0.31030336 0.7569826
#> 2 Q2 -0.09651805 0.9233043
#> 2 Q3 -0.10326583 0.9179609
#> 2 Q4 -0.14107269 0.8880992
#> 3 Q1 -0.23574755 0.8141156
#> 3 Q2 -0.25977019 0.7955805
#> 3 Q3 -0.39411812 0.6943415
#> 3 Q4 -0.38045993 0.7044191
#> 4 Q1 -0.43082365 0.6675332
#> 4 Q2 -0.40476849 0.6865209
#> 4 Q3 -0.42925352 0.6686715
#> 4 Q4 -0.39156135 0.6962239
#> 5 Q1 -0.35314096 0.7247336
#> 5 Q2 -0.47544463 0.6355175
#> 5 Q3 -0.34964305 0.7273493
#> 5 Q4 -0.24700014 0.8054196
#> 6 Q1 -0.25872509 0.7963845
#> 6 Q2 -0.33915908 0.7352083
#> 6 Q3 -0.29083689 0.7717845
#> 6 Q4 -0.24167853 0.8095292
#> 7 Q1 -0.21326793 0.8315566
#> 7 Q2 -0.19229562 0.8479045
#> 7 Q3 -0.14764776 0.8829210
#> 7 Q4 -0.12226792 0.9029347
#> 8 Q1 -0.26173882 0.7940666
#> 8 Q2 -0.38760408 0.6991411
#> 8 Q3 -0.37048701 0.7118112
#> 8 Q4 -0.39610783 0.6928779
#> 9 Q1 -0.39338787 0.6948789
#> 9 Q2 -0.28935025 0.7729184
#> 9 Q3 -0.25478126 0.7994206
#> 9 Q4 -0.33831558 0.7358418
#> 10 Q1 -0.41889724 0.6761987
#>
#> 95 percent confidence intervals for the mean :
#> c.i lower bound c.i upper bound
#> 0 Q1 0.0000000 0.0000000
#> 0 Q2 -0.9641648 0.9425665
#> 0 Q3 -1.4257830 1.4416495
#> 0 Q4 -1.5605692 1.3392499
#> 1 Q1 -1.8571638 1.6142713
#> 1 Q2 -2.0543132 1.6817024
#> 1 Q3 -2.2592728 1.7984069
#> 1 Q4 -2.4420431 1.8571040
#> 2 Q1 -2.6192680 1.9108257
#> 2 Q2 -2.9535331 2.6795248
#> 2 Q3 -3.1200097 2.8113217
#> 2 Q4 -3.2581779 2.8256346
#> 3 Q1 -3.3682944 2.6529071
#> 3 Q2 -3.5193569 2.7045358
#> 3 Q3 -3.6158481 2.4174709
#> 3 Q4 -3.7744966 2.5599165
#> 4 Q1 -3.8978050 2.5071314
#> 4 Q2 -4.0593196 2.6837694
#> 4 Q3 -4.2008595 2.7065518
#> 4 Q4 -4.3492586 2.9156218
#> 5 Q1 -4.4767607 3.1240131
#> 5 Q2 -4.5796877 2.8092101
#> 5 Q3 -4.7139519 3.3015274
#> 5 Q4 -4.8254302 3.7570609
#> 6 Q1 -4.9522934 3.8097917
#> 6 Q2 -5.0793672 3.5964273
#> 6 Q3 -5.2001615 3.8706116
#> 6 Q4 -5.3048691 4.1529076
#> 7 Q1 -5.4136135 4.3628212
#> 7 Q2 -5.5120981 4.5381067
#> 7 Q3 -5.6127304 4.8352823
#> 7 Q4 -5.6694530 5.0113023
#> 8 Q1 -5.8294432 4.4707418
#> 8 Q2 -5.9952332 4.0357457
#> 8 Q3 -6.1064500 4.1848832
#> 8 Q4 -6.2216961 4.1510017
#> 9 Q1 -6.3416464 4.2431255
#> 9 Q2 -6.3854426 4.7601294
#> 9 Q3 -6.4980630 5.0192010
#> 9 Q4 -6.6218240 4.6926658
#> 10 Q1 -6.7627612 4.4050689
esgplotbands(mc.test)
# Correlation test
nb <- 500
s0.par1 <- simshocks(n = nb, horizon = 3, frequency = "semi",
family = 1, par = 0.2)
s0.par2 <- simshocks(n = nb, horizon = 3, frequency = "semi",
family = 1, par = 0.8)
(test1 <- esgcortest(s0.par1))
#> $cor.estimate
#> Time Series:
#> Start = c(0, 2)
#> End = c(3, 1)
#> Frequency = 2
#> [1] 0.17019209 0.09279227 0.18718789 0.22185835 0.14601034 0.19899949
#>
#> $conf.int
#> Time Series:
#> Start = c(0, 2)
#> End = c(3, 1)
#> Frequency = 2
#> Series 1 Series 2
#> 0.5 0.083751429 0.2540906
#> 1.0 0.005143531 0.1790261
#> 1.5 0.101157771 0.2704393
#> 2.0 0.136829774 0.3036416
#> 2.5 0.059076143 0.2307465
#> 3.0 0.113285783 0.2817730
#>
(test2 <- esgcortest(s0.par2))
#> $cor.estimate
#> Time Series:
#> Start = c(0, 2)
#> End = c(3, 1)
#> Frequency = 2
#> [1] 0.7879729 0.7823533 0.8043743 0.7921554 0.7786005 0.8077114
#>
#> $conf.int
#> Time Series:
#> Start = c(0, 2)
#> End = c(3, 1)
#> Frequency = 2
#> Series 1 Series 2
#> 0.5 0.7522620 0.8190677
#> 1.0 0.7458304 0.8141866
#> 1.5 0.7710721 0.8332881
#> 2.0 0.7570532 0.8226977
#> 2.5 0.7415392 0.8109245
#> 3.0 0.7749064 0.8361767
#>
#par(mfrow=c(2, 1))
esgplotbands(test1)
esgplotbands(test2)
