The "prices desticking " property of the weak dollar during shocks

Mishkin's resignation as a Fed Governor was the occasion for the Wall Street Journal to comment his recent views on major topics like the US $ ("nominal exchange rate have exerted small effects on consumer prices" - ref. WSJ).
With all the respect I have for F. Mishkin, I do not share his opinion on the effect of the depreciation of the dollar on inflation.
It is true that in a closed economic system, like the one prevailing before the fall of the Berlin wall and/or in the absence of a supply or demand shock, the (slow) depreciation of the US $ has served the economy of industrialized countries by generating a mild inflation. However, shocks ( oil supply shocks of the 70's or global demand shock of the last 10 years) multiply the effect of the depreciation of the US $ on global inflation.
For an easy illustration of my view, I will use the US $/CHF rate and the Dow Jones commodity index (as a proxy variable for inflation).

Click on chart or a better view.
I read this chart as following:
- in the seventies (oil supply shocks), the dollar value was divided by 2.8 + high commodities prices (and inflation).
- in the 80's and 90's (closed system), $ and commodities were both on a bumpy road ("desynchronised" correlation between the two).
- since 2000 (global demand shock), the $ has lost over 70% of its value + high commodities prices. Emerging countries can fully exploit the structural changes they made since the fall of the Berlin wall. The weakness of the US $ adds up to the extra demand they generate for pushing up commodities prices even higher.

The world does not need a weak US $ for generating a mild inflation right now. The new demands from emerging countries is more than enough for doing the job. Like in the seventies, the weak dollar has a poisonous "prices desticking" property.