The timing correspondence is less than stellar, since the YoY increase in prices for those food items dropped like a rock from October, '08 though Oct. '09. It then shot up to a 7 1/2 year high in May of 2011.
This can be seen in the red line of Graph 1, which also shows the CPI for all items except food and energy (CPILFESL) in blue.
To assume a cause and effect relationship, you have to account for a time lag of a year from the announcement and 6 months from the expansion of QE to the turn around in those price increases from the Oct '09 bottom. Remember, through the first 11 months of QE, the YoY change in those prices dropped dramatically. Between May and November, 2010, while no QE program was in effect, these prices had the steepest part of their rise. After QE II ended in August, 2011, the YoY price increase remained high for those items until the end of the year, and then fell rapidly.
A longer view reveals that the increase in those food prices oscillates continuously around the All Items Less Food and Energy line. The trough to trough period is irregular, averaging 3.52 years with a standard deviation of 0.45 year (5 measurements). The trough to trough time from May, '06 to Oct., '09 was a very typical 3.4 years. It is very hard to look at that graph and see anything unusual about the 2008-2012 region, other than the depth of the trough shortly after the Great Recession.
It appeared to me that the blue line of Graph 1 might be a crude approximation of a long average of the red line. This turns out not quite to be the case, since the two lines are measuring different baskets of goods. What we have is the YoY increase for these food items oscillating around its own mean. That sounds like a tautology, but let's look a little deeper.
Graph 2 shows the same data, along with some long averages of the food stuffs YoY price increase line. These are the 5 Yr (light blue), 8 Yr (yellow), and 13 Yr (purple) moving averages, and the average for the whole data set, 2.9 (bright green). I've also included an envelope one standard deviation (3.06) above (5.96) and below (-0.17) the mean in dark green.
This (sort of) resembles a control chart. The +/- Std. Dev. envelope isn't a hard barrier, but does tend to turn the data path back toward the mean, unless something strange happens. Frex, the big rise from late '02 to early '04 followed the Iraq invasion and resulting disruption in petroleum pricing. The '09 trough was the result of the Great Recession. These are explainable variations.
Note also that the moving average lines tended to run below the CPILFESL line prior to late 2002, and have tended to run above it since. This is to be expected since these items are basically the top of the food chain and have several layers of fuel dependent contributors in their cost structure. Recall that until 2002, fuel prices were low, and since then (except for the Great Recession) have increased steadily.
I'm quite sympathetic to the idea that QE has done very little to help ease the economic doldrums following the GR. But I see no reason at all to believe that it has contributed to the pain and suffering of ordinary citizens at either the grocery store or the gas pump.