I'm currently writing my bachelor thesis and the main goal of my paper is to test if the volatility of single stocks and indices have risen in the past. My data consists of all stocks of the SMI and the DAX. In total, I have 50 stocks with monthly volatility data tested between 2005-2015. So, I have 50 $\times$ 12 $\times$ 10 = 6000 data points. Now I've heard of the time series analysis, ARCH, GARCH(1.1) and GARCH(1.2). I have read a bit about those models, but until now, I have only had 2 statistics courses and 1 econometrics course. And with the knowledge I have at the moment, I cannot understand which model would suit the best and/or is the simplest to model in R/Stata.
I've read that the models ARCH/GARCH are good to model volatility, but it is not the tool to test my hypothesis. Also I've read that those models are mainly to predict future volatility, but my goal is to analyse past volatility, do I still choose ARCH/GARCH?
So my questions are:
- Which model should I use for this kind of hypothesis (hypothesis: Has the volatility of the financial market represented through the SMI and DAX indices risen significantly in the past?)
- If I'd use a time series model like ARCH/GARCH, how do I test my hypothesis?