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Estimation of non-normal GARCH model

The function ugarchfit() does a joint estimation of all the mean, variance and distribution parameters. A general approach is to use a skewed student t distribution. You then need to estimate also the skew and shape parameters \(\xi\) and \(\nu\).

In this exercise, you fit the GARCH model with skewed student t distribution on a simulated return series called ret. The true model used to simulate has the following parameters list(mu = 0, ar1 = 0, ma1 = 0, omega = 6*10^(-7), alpha1 = 0.07, beta1 = 0.9, skew = 0.9, shape = 5)

You will see that you obtain parameter estimates are close to the true parameters. The difference between the estimated and true parameter is called the estimation error. On long time series, the error is typically small.

Diese Übung ist Teil des Kurses

GARCH Models in R

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Anleitung zur Übung

  • Plot the return series ret and note the large negative return.
  • Complete the instructions to specify a GARCH model with skewed student t distribution.
  • Estimate the model.
  • Extract the coefficients from the obtained ugarchfit object.

Interaktive Übung

Versuche dich an dieser Übung, indem du diesen Beispielcode vervollständigst.

# Plot the return series
 ___

# Specify the garch model to be used
garchspec <- ___(mean.model = list(armaOrder = c(0,0)),
                       variance.model = list(model = "sGARCH"),
                        ___ = ___)

# Estimate the model
garchfit <- ___(data = ___, spec = ___)

# Inspect the coefficients
___(___)
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