I am in doubt to understand the notation in this academic article below. This type of notation of equation (1) is not found in the books I study in economics.
For example, in the book of Casella Statististic Inference this notation does not appear and I am having difficulty "reading" this equation.
This type of nottion I will have on Intermediate Probability books?
One of my doubts is to understand how he calculates the conditional expectation of the squared difference between a random variable $x_{t+h}(r)$ and a probability function $p_{s,t+h|t}(r)$ ???
Could you suggest readings to help me better understand these notations? In other articles I also have difficulty understanding notations. I think economics books do not really address these issues.
This is the article:
https://www.ecb.europa.eu/pub/conferences/shared/pdf/20160603_forecasting/Paper_10_Sekhposyan.pdf
Many thanks, guys!