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hngarchSim Simulates a Heston-Nandi Garch(1,1) process,
hngarchFit MLE for a Heston Nandi Garch(1,1) model,
hngarchStats True moments of the log-Return distribution,
print.hngarch Print method,
summary.hngarch Diagnostic summary.}
hngarchSim(model, n, innov, n.start, start.innov, rand.gen, ...)
hngarchFit(x, model = list(lambda = -0.5, omega = var(x), alpha =
0.1 * var(x), beta = 0.1, gamma = 0, rf = 0), symmetric = TRUE,
trace = FALSE, title = NULL, description = NULL, ...)
hngarchStats(model)## S3 method for class 'hngarch':
print(x, \dots)
## S3 method for class 'hngarch':
summary(object, \dots)
innov will be generated using
the random number generator specified by rand.gen.
Missing valulambda,
omega, the constant coefficient of the variance equation,
alpha the autoregressive coefficient,
beta "hngarch"
as returned from the function hngarchFit.rand.gen will be a random number generator.
Additional arguments required by the random number generator
rand.gen, utrace=FALSE, no tracing is done of the
iteration path."hngarch"
as returned from the function hngarchFit.hngarchSim
returns numeric vector with the simulated time
series points neglecting those from the first start.innov
innovations.
hngarchFit
returns list with two entries: The estimated model parmeters
model, where model is a list of the parameters
itself, and llh the value of the log likelihood.
hngarchStats
returns a list with the following components:
persistence, the value of the persistence,
meansigma2, meansigma4, meansigma6, meansigma8,
the expectation value of sigma to the power of 2, 4, 6, and 8,
mean, variance, skewness, kurtosis,
the mean, variance, skewness and kurtosis of the log returns.
summary.hngarch
returns list with the following elements: h,
a numeric vector with the conditional variances, z, a numeric
vector with the innovations.hngarchSim simulates a Heston-Nandi Garch(1,1)
process with structure parameters specified through the list
model(lambda, omega, alpha, beta, gamma, rf).
Parameter Estimation:
The function hngarchFit estimates by the maximum log-likelihood
approach the parameters either for a symmetric or an asymmetric
Heston-Nandi Garch(1,1) model from the log returns x of a
financial time series. For optimization R's optim function is
used. Additional optimization parameters may be passed throught the
... argument.
Diagnostic Analysis:
The function summary.hngarch performs a diagnostic analysis
and recalculates conditional variances and innovations from the time
series.
Calculation of Moments:
The function hngarchStats calculates the first four true
moments of the unconditional log return distribution for a stationary
Heston-Nandi Garch(1,1) process with standard normally distributed
innovations. In addition the persistence and the expectation values
of sigma to the power 2, 4, 6, and 8 can be accessed.## hngarchSim -
# Simulate a Heston Nandi Garch(1,1) Process:
# Symmetric Model - Parameters:
model = list(lambda = 4, omega = 8e-5, alpha = 6e-5,
beta = 0.7, gamma = 0, rf = 0)
ts = hngarchSim(model = model, n = 500, n.start = 100)
par(mfrow = c(2, 1), cex = 0.75)
ts.plot(ts, col = "steelblue", main = "HN Garch Symmetric Model")
grid()
## hngarchFit -
# HN-GARCH log likelihood Parameter Estimation:
# To speed up, we start with the simulated model ...
mle = hngarchFit(model = model, x = ts, symmetric = TRUE)
mle
## summary.hngarch -
# HN-GARCH Diagnostic Analysis:
par(mfrow = c(3, 1), cex = 0.75)
summary(mle)
## hngarchStats -
# HN-GARCH Moments:
hngarchStats(mle$model)Run the code above in your browser using DataLab