I read that the local truncation error of a method of order $p$ is $O(h^{p+1})$ (thus, one order higher). Yet, the global truncation error is in general $O(h^p)$ for a stable method (thus, one order lower than the local error). But why?
If the global truncation error is the accumulation of local truncation error at all steps $h$, shouldn't it be still order $p+1$?