Simulate univariate GARCH/APARCH time series
garchSim.RdSimulates univariate GARCH/APARCH time series.
Usage
garchSim(spec = garchSpec(), n = 100, n.start = 100, extended = FALSE)Arguments
- spec
-
a specification object of class
"fGARCHSPEC"as returned bygarchSpec. See also below for further details. - n
-
length of the output series, an integer value, by default
n=100. - n.start
-
length of ‘burn-in’ period, by default 100.
- extended
-
logical parameter specifying what to return. If
FALSE, return the univariate GARCH/APARCH time series. IfTRUE, return a multivariate time series containing also the volatility and conditional innovations time series.
Details
garchSim simulates an univariate GARCH or APARCH time series
process as specified by argument spec. The default model
specifies Bollerslev's GARCH(1,1) model with normally distributed
innovations.
spec is an object of class "fGARCHSPEC" as returned by
the function garchSpec. It comes with a slot
@model which is a list of just the numeric parameter
entries. These are recognized and extracted for use by the function
garchSim.
One can estimate the parameters of a GARCH process from empirical data
using the function garchFit and then simulate statistically
equivalent GARCH processes with the same set of model parameters using
the function garchSim.
Value
the simulated time series as an objects of
class "timeSeries" with attribute "spec" containing the
specification of the model.
If extended is TRUE, then the time series is
multivariate and contains also the volatility, sigma, and the
conditional innovations, eps.
Note
An undocumented feature (so, it should not be relied on) is that the
returned time series is timed so that the last observation is the day
before the date when the function is executed. This probably should be
controlled by an additional argument in garchSim.
Examples
## garchSpec -
spec = garchSpec()
spec
#>
#> Formula:
#> ~ garch(1, 1)
#> Model:
#> omega: 1e-06
#> alpha: 0.1
#> beta: 0.8
#> Distribution:
#> norm
#> Presample:
#> time z h y
#> 1 0 -0.1207184 1e-05 0
## garchSim -
# Simulate a "timeSeries" object:
x = garchSim(spec, n = 50)
class(x)
#> [1] "timeSeries"
#> attr(,"package")
#> [1] "timeSeries"
print(x)
#> GMT
#> garch
#> 2024-03-11 -2.911226e-03
#> 2024-03-12 2.777206e-03
#> 2024-03-13 2.293454e-03
#> 2024-03-14 -5.724560e-03
#> 2024-03-15 -5.579287e-03
#> 2024-03-16 -3.053223e-03
#> 2024-03-17 -5.901101e-03
#> 2024-03-18 1.982989e-03
#> 2024-03-19 2.311324e-04
#> 2024-03-20 1.591033e-03
#> 2024-03-21 -1.844240e-03
#> 2024-03-22 2.327273e-03
#> 2024-03-23 -2.810579e-03
#> 2024-03-24 4.083679e-03
#> 2024-03-25 -1.981109e-03
#> 2024-03-26 -2.736583e-03
#> 2024-03-27 -3.197631e-03
#> 2024-03-28 -2.687408e-03
#> 2024-03-29 -4.503115e-04
#> 2024-03-30 -9.716603e-04
#> 2024-03-31 1.665776e-03
#> 2024-04-01 -2.800591e-03
#> 2024-04-02 1.205845e-03
#> 2024-04-03 8.911127e-04
#> 2024-04-04 -3.355605e-03
#> 2024-04-05 6.375044e-04
#> 2024-04-06 6.992214e-03
#> 2024-04-07 2.302707e-03
#> 2024-04-08 -2.773734e-05
#> 2024-04-09 -6.103604e-03
#> 2024-04-10 -2.646679e-03
#> 2024-04-11 9.828453e-04
#> 2024-04-12 2.199372e-03
#> 2024-04-13 -1.669151e-03
#> 2024-04-14 4.976765e-04
#> 2024-04-15 1.773448e-03
#> 2024-04-16 4.240135e-04
#> 2024-04-17 2.872468e-03
#> 2024-04-18 -4.483632e-03
#> 2024-04-19 4.522951e-03
#> 2024-04-20 -5.253080e-03
#> 2024-04-21 1.227027e-03
#> 2024-04-22 5.491888e-03
#> 2024-04-23 -2.600418e-03
#> 2024-04-24 2.780861e-03
#> 2024-04-25 3.701203e-03
#> 2024-04-26 6.088748e-03
#> 2024-04-27 -1.635551e-03
#> 2024-04-28 1.800426e-03
#> 2024-04-29 5.328106e-03
## More simulations ...
# Default GARCH(1,1) - uses default parameter settings
spec = garchSpec(model = list())
garchSim(spec, n = 10)
#> GMT
#> garch
#> 2024-04-20 1.106146e-03
#> 2024-04-21 4.758933e-03
#> 2024-04-22 -4.830058e-03
#> 2024-04-23 -1.673998e-03
#> 2024-04-24 4.252527e-03
#> 2024-04-25 1.028559e-03
#> 2024-04-26 -1.439446e-03
#> 2024-04-27 6.829775e-05
#> 2024-04-28 5.870645e-03
#> 2024-04-29 3.393152e-03
# ARCH(2) - use default omega and specify alpha, set beta=0!
spec = garchSpec(model = list(alpha = c(0.2, 0.4), beta = 0))
garchSim(spec, n = 10)
#> GMT
#> garch
#> 2024-04-20 0.0057975767
#> 2024-04-21 -0.0011834665
#> 2024-04-22 0.0017927422
#> 2024-04-23 -0.0008625608
#> 2024-04-24 0.0010001187
#> 2024-04-25 0.0030832726
#> 2024-04-26 -0.0018462440
#> 2024-04-27 -0.0023798962
#> 2024-04-28 0.0008704696
#> 2024-04-29 0.0007833472
# AR(1)-ARCH(2) - use default mu, omega
spec = garchSpec(model = list(ar = 0.5, alpha = c(0.3, 0.4), beta = 0))
garchSim(spec, n = 10)
#> GMT
#> garch
#> 2024-04-20 -0.0064929453
#> 2024-04-21 -0.0034116707
#> 2024-04-22 -0.0007531555
#> 2024-04-23 -0.0022603821
#> 2024-04-24 -0.0018410996
#> 2024-04-25 -0.0006229702
#> 2024-04-26 -0.0003279921
#> 2024-04-27 0.0012915726
#> 2024-04-28 0.0019140520
#> 2024-04-29 0.0005515873
# AR([1,5])-GARCH(1,1) - use default garch values and subset ar[.]
spec = garchSpec(model = list(mu = 0.001, ar = c(0.5,0,0,0,0.1)))
garchSim(spec, n = 10)
#> GMT
#> garch
#> 2024-04-20 0.0032399130
#> 2024-04-21 0.0022705751
#> 2024-04-22 -0.0002870203
#> 2024-04-23 -0.0011077627
#> 2024-04-24 -0.0031293745
#> 2024-04-25 -0.0017970990
#> 2024-04-26 0.0037490018
#> 2024-04-27 0.0057034846
#> 2024-04-28 0.0036035562
#> 2024-04-29 0.0039249405
# ARMA(1,2)-GARCH(1,1) - use default garch values
spec = garchSpec(model = list(ar = 0.5, ma = c(0.3, -0.3)))
garchSim(spec, n = 10)
#> GMT
#> garch
#> 2024-04-20 0.0043355134
#> 2024-04-21 0.0017659100
#> 2024-04-22 -0.0001591027
#> 2024-04-23 0.0019475098
#> 2024-04-24 -0.0010304484
#> 2024-04-25 -0.0030496409
#> 2024-04-26 0.0052197228
#> 2024-04-27 0.0022934947
#> 2024-04-28 0.0044816948
#> 2024-04-29 0.0024859766
# GARCH(1,1) - use default omega and specify alpha/beta
spec = garchSpec(model = list(alpha = 0.2, beta = 0.7))
garchSim(spec, n = 10)
#> GMT
#> garch
#> 2024-04-20 -0.0021716014
#> 2024-04-21 -0.0010676195
#> 2024-04-22 -0.0030764296
#> 2024-04-23 -0.0037004641
#> 2024-04-24 0.0004573765
#> 2024-04-25 0.0018448483
#> 2024-04-26 -0.0021326537
#> 2024-04-27 0.0010830056
#> 2024-04-28 -0.0026793967
#> 2024-04-29 0.0014976260
# GARCH(1,1) - specify omega/alpha/beta
spec = garchSpec(model = list(omega = 1e-6, alpha = 0.1, beta = 0.8))
garchSim(spec, n = 10)
#> GMT
#> garch
#> 2024-04-20 0.0017863687
#> 2024-04-21 0.0008059858
#> 2024-04-22 0.0032089856
#> 2024-04-23 0.0038018231
#> 2024-04-24 0.0022089156
#> 2024-04-25 -0.0007191500
#> 2024-04-26 -0.0004469074
#> 2024-04-27 0.0006013883
#> 2024-04-28 -0.0019554465
#> 2024-04-29 -0.0010905864
# GARCH(1,2) - use default omega and specify alpha[1]/beta[2]
spec = garchSpec(model = list(alpha = 0.1, beta = c(0.4, 0.4)))
garchSim(spec, n = 10)
#> GMT
#> garch
#> 2024-04-20 0.0019340643
#> 2024-04-21 0.0000668850
#> 2024-04-22 0.0010577411
#> 2024-04-23 -0.0016142765
#> 2024-04-24 0.0006535521
#> 2024-04-25 0.0008639688
#> 2024-04-26 0.0026345660
#> 2024-04-27 -0.0010614920
#> 2024-04-28 -0.0011161853
#> 2024-04-29 0.0004583598
# GARCH(2,1) - use default omega and specify alpha[2]/beta[1]
spec = garchSpec(model = list(alpha = c(0.12, 0.04), beta = 0.08))
garchSim(spec, n = 10)
#> GMT
#> garch
#> 2024-04-20 -8.562066e-05
#> 2024-04-21 -2.033166e-03
#> 2024-04-22 -9.540200e-04
#> 2024-04-23 3.912605e-04
#> 2024-04-24 -1.887491e-03
#> 2024-04-25 -1.231150e-04
#> 2024-04-26 1.352201e-03
#> 2024-04-27 7.294251e-04
#> 2024-04-28 2.526151e-03
#> 2024-04-29 4.799199e-04
# snorm-ARCH(1) - use defaults with skew Normal
spec = garchSpec(model = list(beta = 0, skew = 0.8), cond.dist = "snorm")
garchSim(spec, n = 10)
#> GMT
#> garch
#> 2024-04-20 -7.485606e-04
#> 2024-04-21 8.914988e-04
#> 2024-04-22 -5.381224e-04
#> 2024-04-23 2.703609e-04
#> 2024-04-24 -6.094172e-04
#> 2024-04-25 1.043383e-03
#> 2024-04-26 4.731667e-04
#> 2024-04-27 1.054015e-03
#> 2024-04-28 -5.737206e-04
#> 2024-04-29 -7.588362e-05
# sged-GARCH(1,1) - using defaults with skew GED
model = garchSpec(model = list(skew = 0.93, shape = 3), cond.dist = "sged")
garchSim(model, n = 10)
#> GMT
#> garch
#> 2024-04-20 -0.0002272700
#> 2024-04-21 0.0027759594
#> 2024-04-22 0.0013211663
#> 2024-04-23 0.0015949448
#> 2024-04-24 0.0020719752
#> 2024-04-25 0.0031343476
#> 2024-04-26 0.0020836428
#> 2024-04-27 -0.0020425228
#> 2024-04-28 -0.0002816032
#> 2024-04-29 -0.0011687944
# Taylor Schwert GARCH(1,1) - this belongs to the family of APARCH Models
spec = garchSpec(model = list(delta = 1))
garchSim(spec, n = 10)
#> GMT
#> garch
#> 2024-04-20 -4.009875e-06
#> 2024-04-21 -7.730200e-06
#> 2024-04-22 9.493940e-06
#> 2024-04-23 1.129811e-06
#> 2024-04-24 1.523020e-05
#> 2024-04-25 -1.575024e-06
#> 2024-04-26 -7.708138e-06
#> 2024-04-27 -1.477749e-06
#> 2024-04-28 -8.557498e-06
#> 2024-04-29 -5.101195e-06
# AR(1)-t-APARCH(2, 1) - a little bit more complex specification ...
spec = garchSpec(model = list(mu = 1.0e-4, ar = 0.5, omega = 1.0e-6,
alpha = c(0.10, 0.05), gamma = c(0, 0), beta = 0.8, delta = 1.8,
shape = 4, skew = 0.85), cond.dist = "sstd")
garchSim(spec, n = 10)
#> GMT
#> garch
#> 2024-04-20 0.0001359655
#> 2024-04-21 0.0005524952
#> 2024-04-22 0.0018123402
#> 2024-04-23 -0.0079753569
#> 2024-04-24 -0.0187944795
#> 2024-04-25 -0.0103353483
#> 2024-04-26 -0.0088322302
#> 2024-04-27 -0.0128158606
#> 2024-04-28 0.0044420012
#> 2024-04-29 0.0004834796
garchSim(spec, n = 10, extended = TRUE)
#> GMT
#> garch sigma eps
#> 2024-04-20 -0.0039057370 0.001831888 -2.6544277
#> 2024-04-21 -0.0030935270 0.002266588 -0.5473682
#> 2024-04-22 -0.0025168619 0.002376449 -0.4502931
#> 2024-04-23 0.0011837586 0.002230510 1.0500689
#> 2024-04-24 0.0015200149 0.002207861 0.3750850
#> 2024-04-25 0.0023305544 0.002124541 0.6921715
#> 2024-04-26 0.0008536017 0.002035029 -0.2022946
#> 2024-04-27 -0.0004914010 0.001923368 -0.5293849
#> 2024-04-28 0.0009323699 0.001827788 0.5898224
#> 2024-04-29 -0.0062338241 0.001766998 -3.8483397