QuoteOriginally posted by: NDistribution = PDF(x).Stationary = PDF is not a function of t.If we have PDF(x,t) that's not a distribution.If we are taking about finance, instead of arguing pure math for the sake of it, then this is a Humpty-Dumpty argument. ("When I use a word it means just what I want it to mean"). I have never had much interest in pure math, but I'm very good at finding simple math to describe complex real-life problems. I rarely need much more than undergraduate calculus and algebra. So forgive me if you find it tiresome to bring this discussion back to earth; I couldn't join you up in the clouds even if I tried.A variable transformation y = Y(x,t) converts a stationary PDF into a non-stationary one or vice versa. It's the stationarity of the model used for the time series (i.e. getting the time-dependence of the PDF right -- or as right as does the job) that matters, not stationarity of the PDF itself. Alternatively and equivalently, it's about finding the variable for which the empirical PDF is effectively stationary.To bandy terms like stationary about without specifying context is just as silly as using words like random and deterministic without specifying variables. So when you're ready, N, to specify which variables are deterministic or have a stationary PDF, I'm all ears.
Last edited by Fermion
on May 8th, 2007, 10:00 pm, edited 1 time in total.