Dollar Down, Gold Up?

We're not the best observers of the dollar/gold relationship.  However, We have noticed some discussion of the idea that if the dollar declines then the price of gold will (continue to) rise.  This logic seem to make perfect sense, on the surface.  However, we couldn't help but notice that when viewed over a long period of time the idea of gold going up while the dollar is going down doesn't add up.
In the chart below, we see point A as the peak in the price of gold (red line) and point B as the trough.  Correspondingly, we have the trade weighted dollar (blue line) with point C being the peak and point D as the trough.  Because the period of time that lapsed was nearly ten years when the "price" of both the dollar and gold declined at the same time, it seems challenging to cling to the belief that if one falls the other rises in value.
1973-2001
Interestingly, in the period before point A, both indexes rose for a short while.  During points A-C and D-B there was an inverse relationship.  Additionally, the period from 2001 to the present has maintained an inverse relationship with the price of gold going up while the dollar has fallen.

Overall, the number of years that there is a correlation between the dollar and gold is almost the same as the inverse relationship.  Because of the inconsistency of the relationship between gold and the dollar, the "obvious" conclusion doesn't seem to fit.

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