Description Usage Arguments Details Value Note Author(s) See Also Examples
svsim
is used to produce realizations of a stochastic volatility (SV)
process.
1 
len 
length of the simulated time series. 
mu 
level of the latent logvolatility AR(1) process. The defaults
value is 
phi 
persistence of the latent logvolatility AR(1) process. The
default value is 
sigma 
volatility of the latent logvolatility AR(1) process. The
default value is 
nu 
degreesoffreedom for the conditional innovations distribution.
The default value is 
rho 
correlation between the observation and the increment of the
logvolatility. The default value is 
This function draws an initial logvolatility h_0
from the stationary
distribution of the AR(1) process defined by phi
, sigma
, and mu
.
Then the function jointly simulates the logvolatility series
h_1,...,h_n
with the given AR(1) structure, and the “logreturn” series
y_1,...,y_n
with mean 0 and standard deviation exp(h/2)
.
Additionally, for each index i
, y_i
can be set to have a conditionally heavytailed
residual (through nu
) and/or to be correlated with (h_{i+1}h_i)
(through rho
, the socalled leverage effect, resulting in asymmetric “logreturns”).
The output is a list object of class svsim
containing
y 
a vector of length 
vol 
a vector of length

vol0 
The initial volatility 
para 
a named list with five elements 
The function generates the “logreturns” by
y < exp(h/2)*rt(h, df=nu)
. That means that in the case of nu < Inf
the (conditional) volatility is sqrt(nu/(nu2))*exp(h/2)
, and that corrected value
is shown in the print
, summary
and plot
methods.
To display the output use print
, summary
and plot
. The
print
method simply prints the content of the object in a moderately
formatted manner. The summary
method provides some summary statistics
(in %), and the plot
method plots the the simulated 'logreturns'
y
along with the corresponding volatilities vol
.
Gregor Kastner gregor.kastner@wu.ac.at
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  ## Simulate a highly persistent SV process of length 500
sim < svsim(500, phi = 0.99, sigma = 0.1)
print(sim)
summary(sim)
plot(sim)
## Simulate an SV process with leverage
sim < svsim(200, phi = 0.94, sigma = 0.15, rho = 0.6)
print(sim)
summary(sim)
plot(sim)
## Simulate an SV process with conditionally heavytails
sim < svsim(250, phi = 0.91, sigma = 0.05, nu = 5)
print(sim)
summary(sim)
plot(sim)

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