Quantifying volatility: a step by step approach?

Question

I am a former electronics engineer and I'm fairly new to financial time series analysis. I'm currently working on a thesis on copper determinants and what factors influence its price from an economic perspective. I'd like quantify its volatility over time in order to show the complexity of its price forecasting.

Alternative techniques for forecasting mineral commodity prices from Tapia Cortez et al. conclude that time series modelling is somewhat limited for mineral commodities price forecasting.

I think I understand the maths behind ARCH/GARCH models but I lack financial knowledge. There are several tutorials on how to apply these models but very few in my opinion on why we use them. My prior idea would be showing that there is conditional heteroskedasticity. Am I right ? How would I test this assumption ? I am getting confused on which tools and models would be used to infer my hypothesis.

Answer 1

Indeed, one of the purposes of ARCH/GARCH is to model the volatility of a time series using past values of the times series. If you fit an ARCH/GARCH model, then you are going to estimate coefficients which determine how the volatility of your process at time $t$ depends on previous observations of your time series. If you see that none of these coefficients are significantly different than 0, then you could assume that there is no heteroscedasticity (or at least that it is not determined by the dependent variables you have used in your model). If at least one coefficient is significantly different from 0, then it would be a good indicator that there is indeed heteroscedasticity in your time series.