Simulating a series with univariate GARCH(1,1) conditional variances

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Description

This function simulates an univariate time series with GARCH(1,1) conditional variances.

Usage

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    uni.vola.sim(a, nobs, d.f=Inf, cut=1000)

Arguments

a

a vector of parameters (3 \times 1)

nobs

a number of observations simulated (T)

d.f

degrees of freedom parameter for t-distribution

cut

a number of observations to be removed to minimise the initial effects

Value

A list with components:

h

GARCH(1,1) conditional variances (T \times 1)

eps

a series of error term with the conditional variances "h" (T \times 1)

Note

When d.f=Inf, the innovations (the standardised residuals) follow the standard normal distribution. Otherwise, they follow a student's t-distribution with d.f degrees of freedom.

References

Bollerslev, T. (1986), “Generalized Autoregressive Conditional Heteroskedasticity”, Journal of Econometrics, 31, 307–327.

Fiorentini, G., G. Calzolari and L. Panattoni (1996), “Analytic Derivatives and the Computation of GARCH Estimates”, Journal of Applied Econometrics, 11, 399–417.

See Also

uni.vola

Examples

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nobs <- 1000
nu <- 8
a <- c(0.1,0.2,0.7)           #  a <- c(a constant, ARCH parameter, GARCH parameter) 
# with normal innovations
eps <- uni.vola.sim(a, nobs)
# with t innovations
eps.t <- uni.vola.sim(a, nobs, d.f = df)

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