(d). Fit the return data with the following GJR model:yt = µ + utut = vtσtσ2t = α0 + α1u2t−1 + β1σ2t−1 + γu2t−1It−1Write down the estimated model. Hint: Search the function ‘ugarchfit’ in the package‘rugarch’. You can first specify the GJR model as:ugarchspec(variance.model=list(model=’gjrGARCH’), mean.model=list(armaOrder=c(0,0)))Then use ugarchfit to estimate the specified model.(e). Is there leverage effect according to the evidence suggested by the GJR model? Specifyyour reason.
Question
(d). Fit the return data with the following GJR model:yt = µ + utut = vtσtσ2t = α0 + α1u2t−1 + β1σ2t−1 + γu2t−1It−1Write down the estimated model. Hint: Search the function ‘ugarchfit’ in the package‘rugarch’. You can first specify the GJR model as:ugarchspec(variance.model=list(model=’gjrGARCH’), mean.model=list(armaOrder=c(0,0)))Then use ugarchfit to estimate the specified model.(e). Is there leverage effect according to the evidence suggested by the GJR model? Specifyyour reason.
Solution
The question is asking to fit a GJR-GARCH model to some return data and then determine if there is a leverage effect. Here's a step-by-step guide on how to do this in R using the 'rugarch' package:
Step 1: Install and load the 'rugarch' package. If you haven't installed it yet, you can do so with the command install.packages('rugarch'). Then load the package with library(rugarch).
Step 2: Specify the GJR-GARCH model. You can do this with the ugarchspec function. The command would look like this:
spec = ugarchspec(variance.model = list(model = 'gjrGARCH'), mean.model = list(armaOrder = c(0, 0)))
Step 3: Fit the model to your data. You can do this with the ugarchfit function. You'll need to replace 'data' with your actual data:
fit = ugarchfit(spec, data)
Step 4: Write down the estimated model. You can view the model parameters with the command coef(fit).
Step 5: Determine if there is a leverage effect. The leverage effect is indicated by the γ parameter in the GJR-GARCH model. If γ is statistically significant (p-value < 0.05), then there is evidence of a leverage effect. You can check the p-value of γ with the command fit@fit$matcoef[5,4].
Remember to replace 'data' with your actual return data.
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