# Testing if volatility increases during ECB-Monetary Press Releases

I'm currently writing a thesis where I am trying to disect the ECB monetary press releases and their impact on the European stock market. I am using an event study methodology. Computing Daily Excess returns on indices and testing on those on event days are going fine. Now I have reached the point in my analysis where I focus on the volatility and whether this increases on the day of these releases or not. I would also like to conduct analysis of whether it increases on the day before and after. The problem is I do not know how to exactly do this.

I have seen people suggest GARCH(1,1) models when trying to do event studies on volatility the problem is I do not know exactly how to do this. My hypothesis is that volatility increases during these events but I do not know how to test this. So my questions are:

1. Which model should I use to test this hypothesis (Hypothesis: Volatility in the European stock market increases on ECB Monetary policy announcement days). If I use this model how do I test my hypothesis?
2. Is it possible for me to add other variables than the dummy variables for my event days (I would also like to test if shocks in monetary policy or changes in interest rates has an effect).
3. Perhaps I can also do simple OLS regressions with a measure of volatility as my $$y$$ variable and the event day as my dummy variable?

Note: I primarily use Stata for my analysis.

1. Which model should I use to test this hypothesis (Hypothesis: Volatility in the European stock market increases on ECB Monetary policy announcement days). If I use this model, how do I test my hypothesis?

Using a GARCH model with a dummy in the conditional variance equation sounds like a good approach. The conditional variance equation is $$\sigma_t^2=\omega+\alpha_1\varepsilon_{t-1}^2+\beta_1\sigma_{t-1}^2+\gamma d_t$$ where $$d_t$$ is the dummy variable. Test $$H_0\colon \gamma=0$$ using a $$t$$-test. If you reject $$H_0$$, you have an indication for presence of an effect on the conditional variance.

1. Is it possible for me to add other variables than the dummy variables for my event days? I would also like to test if shocks in monetary policy or changes in interest rates has an effect.

Yes, you can add more variables to the equation.

1. Perhaps I can also do simple OLS regressions with a measure of volatility as my $$y$$ variable and the event day as my dummy variable?

You could do this, but I think GARCH is a more elegant approach. Obtaining an accurate and precise measure of volatility to use as $$y$$ in an OLS regression is quite challenging, especially in presence of external shocks that you wish to test for. Meanwhile, in GARCH the measure is embedded in the model itself. (I do not have a good way to explain this now, but I will update the answer if I come up with anything relevant.)

• Thank you very much @Richard for your response, I think I will continue my analysis using the Garch (1,1) model to test whether the volatility changes during my event. A few follow up questions: 1. Is it possible to add a continuous variable such as the difference between implied futures rate at time t and t-1 to use as a proxy for monetary shocks? 2. Is it possible to use the model you specified but also add two more terms to test for the volatility the day before the event and the day after. 3. Are there any important tests I need to do before I try to use the models? Commented May 12, 2023 at 2:13
• @kronow, 1. Yes, this is possible. There is one nuance here: we want volatility to stay positive, but some variables can be negative and thus drag the volatility into the negative territory, too. For that, log-GARCH or EGARCH may be used instead of GARCH, as they ensure positivity. 2. Yes, this is possible. 3. Not really, but you may want to do diagnostic testing of the model once you have fit it. The standardized residuals should be i.i.d. and have the distribution that you assumed in your model. If you find deviations from these properties, you may want to tweak the model to get rid of them. Commented May 12, 2023 at 7:23
• @kronow, more about log-GARCH or EGARCH instead of GARCH: these models are a bit harder to interpret, so often we just do vanilla GARCH for simplicity. We thus take the risk of obtaining negative predicted volatility in the future. The fitting routine should ensure it is positive in sample, but there are no guarantees about predictions out of sample. Commented May 12, 2023 at 7:26
• I just thought to perhaps take the absolute differences in these futures in regards to question 1, perhaps that might be a solutions? @Richard Commented May 12, 2023 at 7:30
• @kronow, that depends on whether it makes subject-matter (economic, financial) sense. Commented May 12, 2023 at 8:06