Official inflation numbers include a large number of components - one way to look at them is to classify in terms of core and non-core, or going one step further "sticky" versus "flexible". Sticky prices are the non-volatile things that tend to have much more stable pricing i.e., rents, insurance, services in general, medical care. Volatile goods tend to be commodity based (energy, foods, etc).
The last 5 years have seen a high impact on CPI from the fall in volatile commodities, driven by two trends- low pricing pressure from the employment market, and large falls in the real price of commodities. This has masked the strong trend in "stick" inflation which has been increasing since the end of 2013 and now running at a rate of close to 2.5% per annum.
Price pressures in the employment market have turned and there is increasing employment costs evident. Commodities appear to have bottomed and there is only a low probability of sustained lower prices. The five years of deflationary pressures are coming to an end - expect to see inflation, particularly in the US become a major talking point as we move into 2016. Portfolios of equities and real assets can perform very well in an inflationary and/or a rising rate environment so we do not see this as negative for equity and commodity markets, as long as rate hikes are accompanied by solid US growth, markets should take them in their stride.
A good discussion of the "Sticky Price" effect from the Cleveland Fed (published in 2010) can be found here:
“Are Some Prices in the CPI More Forward Looking than Others? We Think so”: