Can PPP adjusted values be compared over time?
There are two questions here:

Whether it is meaningful to compare PPP-adjusted values intertemporaly

Whether the &quot;Big Mac&quot; index is a good index for PPP-adjustment.


I will occupy myself with the first question.
Why are we doing PPP-adjustment? We do it to make inter-country comparisons against a benchmark country (usually the US). So this country's magnitude remains unadjusted. Note that what we adjust is nominal magnitudes not &quot;real&quot; ones (that are magnitudes adjusted of in-country inflation).
So at time $t$, and using country $A$ as the benchmark, we can obtain the PPP-wage of country $B$, say $\bar w_{B|A}(t)$. We could think of that as &quot;I live in country B. My living standard at time $t$ is as if I was living in the benchmark country $A$ and my wage was $\bar w_{B|A}(t)$&quot;. And comparing that to the actual (nominal) average wage in country $A$, $w_A(t)$, we get a measure of the living standards in country $B$ compared to those in the benchmark country $A$.
Consider now the PPP-adjusted wage from the same country at time $t+k$. It says &quot; I am living in country B in period $t+k$. My living standard at time $k+t$ is as if I I was living in the benchmark country $A$ and my wage was $\bar w_{B|A}(t+k)$&quot;.
It is evident that in order to meaningfully compare $\bar w_{B|A}(t)$ and $\bar w_{B|A}(t+k)$, we must deflate the latter by the price deflator of the benchmark country A, covering the period $(t,\, t+k)$. Doing that, makes the two comparable.
But the main purpose of PPP-adjustment is inter-country coparisons, not same-country intertemporal comparisons. By considering the ratio in two different time periods,
$$\frac{\bar w_{B|A}(t)}{ w_A(t)},\qquad \frac{\bar w_{B|A}(t+k)}{w_A(t+k)}, $$
we can see whether living standards have converged or diverged.
A discussion on recent PPP issues can be downloaded here.
A visual tool can be accessed here.