Before undertaking a more complex time series approach like VAR, I have attempted some more basic approaches. Again, the aim is to determine the relationship of Hg prices and Au prices after taking into account a generic metals price index.
First, I ran a cross-correlation of the mercury and gold price series. The highest correlation was a lag-0, so I decided to ignore time lags for now.
Then, I ran correlations (pearson) on each pair of variables (e.g. mercury~gold). I found that mercury and gold prices were correlated more strongly (~0.9) than either mercury or gold were correlated with the price index (~0.6 and ~0.5 respectively).
Next, I created 3 linear regression models: (hg~au), (hg~price index), and (hg~au + price index). The last mode showed the highest R2, with au contributing most to the fit, but the price index also making a statistically significant contribution.
I concluded that mercury and gold prices are correlated much more strongly to each other than to a generic price index, and that a linear model including both gold price and metals price index provided the best prediction for mercury prices.
I would be very grateful for any feedback or criticism. Would VAR add significant value to this?