PPP are a snapshot on the situation at a particular point in time. Looking at their series and their volatility, I have the feeling PPP are not comparable along time; or at least, we are lacking some additional factor not yet included in our analysis. Indeed, GDPs are easily comparable in tradables. Non-tradables are the thing PPP is dealing with. In order to make a series, we need a deflactor. If trend prices of tradables are different from trend of non-tradables, the series on PPP can't be built.
I remember the first projections gave the year 2050 for China to surpass USA; there was even a page on The Economist for that bet (it should be still accesable). The most recent projection, made perhaps only one or two years ago, was 2017; and suddenly it happened this year. We are lacking some factor!