咨询在Tsay的GARCH-in-Mean代码中添加dummy variable的位置以测试其影响

First, let's break down where to insert dummy variables based on what effect you want to test (mean equation vs. variance equation) — since the GARCH-in-Mean (GARCH-M) model has two core components: the mean equation (which includes the conditional variance term) and the variance (GARCH) equation.

1. Prepare Your Dummy Variable #

First, define your dummy variable (e.g., a 0-1 vector for event periods) to match the length of your return series (rt in the original code). For example:

# Example: Dummy = 1 for periods 50-100 (event window), 0 otherwise
dummy <- rep(0, length(rt))
dummy[50:100] <- 1

2. Add Dummy to the Mean Equation (Test Impact on Returns/GARCH-M Effect) #

If you want to test whether the dummy affects average returns (or interacts with the GARCH-M term), modify the mean.model argument in ugarchspec to include the dummy as an external regressor. This inserts the dummy directly into the mean equation:

# Modified specification with dummy in mean equation
spec <- ugarchspec(
  variance.model = list(garchOrder = c(1,1)),
  mean.model = list(
    armaOrder = c(0,0), 
    archm = TRUE,  # Keeps the GARCH-in-Mean term enabled
    archpow = 1,
    external.regressors = as.matrix(dummy)  # Insert dummy here
  )
)

# Fit the updated model
fit <- ugarchfit(spec = spec, data = rt)

After fitting, run summary(fit) to check the dummy's coefficient significance — a small p-value means the dummy has a meaningful impact on the mean return alongside the GARCH-M term.

If you want to test an interaction between the dummy and the GARCH-M term, create an interaction variable and add it to the external regressors:

# Create interaction term: dummy * conditional volatility proxy
# (Use sigma from an initial basic GARCH-M fit for this example)
basic_fit <- ugarchfit(ugarchspec(variance.model = list(garchOrder = c(1,1)), mean.model = list(armaOrder = c(0,0), archm = TRUE)), data = rt)
interact_term <- dummy * sqrt(basic_fit@fit$sigma2)

# Update spec with both dummy and interaction term
spec_interact <- ugarchspec(
  variance.model = list(garchOrder = c(1,1)),
  mean.model = list(
    armaOrder = c(0,0), 
    archm = TRUE,
    archpow = 1,
    external.regressors = cbind(dummy, interact_term)
  )
)
fit_interact <- ugarchfit(spec = spec_interact, data = rt)

3. Add Dummy to the Variance Equation (Test Impact on Volatility) #

To test if the dummy affects volatility dynamics (the GARCH component), add the dummy to the variance.model instead:

# Modified specification with dummy in variance equation
spec_vol <- ugarchspec(
  variance.model = list(
    garchOrder = c(1,1),
    external.regressors = as.matrix(dummy)  # Insert dummy here
  ),
  mean.model = list(
    armaOrder = c(0,0), 
    archm = TRUE, 
    archpow = 1
  )
)

fit_vol <- ugarchfit(spec = spec_vol, data = rt)

Check the variance equation coefficients in summary(fit_vol) — a significant dummy coefficient means the event captured by the dummy changes the volatility behavior of the series.

Key Notes #

• Ensure your dummy variable has no missing values and matches the length of your return data exactly.
• For multiple dummies, pass a matrix (e.g., cbind(dummy1, dummy2)) to external.regressors.
• Run diagnostic tests (like ARCH tests on residuals) to confirm the model still fits well after adding the dummy.

内容的提问来源于stack exchange，提问作者NSF