Testing if the volatility of single stocks and/or indices have risen in the past.

Hey Guys,

I'm an economics and business student from Basel(Switzerland), and I'm currently writing my bachelor thesis in "Corporate Financial Management". The title of my thesis is: Is There A Change In The Long Term Trend Of Stock Markets?

However 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 betwenn 2005-2015. So, I have 50x12X10= 6000 Datas. 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.

Also I've read that those models are good to model volatility, but a friend of mine told, that I don't test my hypothesis witch those models.

So my questions is: Which model should I use, and how can I regress my dataset to test the hypothesis/ how do I test my hypothesis efficiently with this data set.

PS: Sorry for any English mistakes, it's not my native language. I'm thanking in advance, for all the people taking their time, to answer my question.

Have a nice day.