In finance, it is well-known that the expected value of asset returns, $\mu$, otherwise known as the average return or mean or first statistical moment, is difficult to predict. I think it was Mandelbrot or Merton who first showed proof of this.
Could someone summarise how, and what is the procedure, for evaluating the accuracy and precision of predictions made of a time series' first statistical moment (which is a scalar value), based on historical returns data? Is it simply the prediction compared to the actual mean when the new data arrives?
And if there are multiple models individually giving a unique prediction of the asset mean, how can these different predictions be compared against one another? Would the comparison be really against one another, or each against some sort of truth benchmark like the true mean, if obtainable?