I have difficulties with under understanding the idea that Diebold came up with in 1998 in his essay about the evaluation of the accuracy of forecasting density p(y), he used the probability integral transform first to define that a variable Z:
and then he defined the density of Z, which is the following thing:
According to him, f(y) is the true density of yt, which is never known by us,and p(t) is the estimated density of yt. I don't really understand how to get the density of Z and it seems the above process not make sense for me, can somebody explain how this is derived? Thanks!
