Recently, I have been studying the relationship between COVID-19 and stock returns using a GJR form of threshold ARCH model. However, I got some unusual estimation results I can't figure out whether they are fine or not. The model I have estimated is written below:
In the equation, D1 is 0 before the pandemic and 1 during the pandemic. I used the following command in STATA for obtaining the result:
arch djones covid19, arch(1/1) tarch(1/1) garch(1/1) het(covid19)
The estimation results of the above models show negative intercept terms, α in the volatility equation (-2.97). However, the estimated intercept is significant at 1%. Full results are shown below:
Furthermore, in the case of S&P500, the sum of alpha1 and beta1 also would be negative but significant.
However, when I remove the dummy term and focus on GARCH(1,1) model in the equation written above, the problem gets solved mostly. But I won't be able to study the impacts of COVID-19 on stock returns. I also checked AIC and BIC and found that still, the GJR-GARCH model has lower BIC than that of the standard GARCH model.
My question is how to deal with this type of problem? Can the negative intercept term still valid if it is significant? or
- Do I ignore the intercept of the volatility equation?
- Should I conduct two GARCH models separately: one for before the pandemic and another during the pandemic?
I would be thankful if you could provide some insights on it.
Thank you.
het()
enters the variables as multiplicative heteroskedasticity and thus you get $\exp(\alpha_0 + \gamma_1 \cdot \text{covid19})$ per your above code. [1/2] $\endgroup$arch djones covid19
is written in the documentation as $djones_t = \beta_0 + \beta_1 \cdot \text{covid19}_t$. I just want you to verify whether equation (2) and (3) are the exact same as the model you're estimating using the STATA code. $\endgroup$