I wish to find the z-score of a value measure( e/g P/E ratio) to compare them across asset classes, currently i am using an expanding window z-score to calculate the long-term mean and standard deviation upto that point in time. But the problem with that is my z-scores vary by quite a lot if a start my backtesting from 1999 vs if I start my backtesting from 2001. If a value measure was completely mean-reverting this would not have ideally happened.
So currently I am thinking of calculating the half-life of a particular value measure and use a rolling window z-score with that half life. But i am sure that may be better ways of solving this problem (because the half life would also vary with time) and i'd appreciate some inputs.