DislikedThe market return is not Normally distributed but somewhere between Cauchy and Student distributed. Kalman filter performances degrade quickly for non-Normal innovations. That's why I use another Kalman filter which estimates the error of the first one and I feedback this information into the first model as a modulation of the allowed variance of the state. A kind of dynamic cursor "lag <-> smoothness". This first model is a second order polynomial local estimation. I chose a 2nd order polynomial because it can approximate (Taylor) any smooth function...Ignored

Are you talking about ARMA processes which generate the price movements? I tried before to get a time series estimation for daily data on GBPUSD, partial autocorrelation showed significant coefficient only for Y(t-1) (partial autocorrelation of Y and Y(t-1)), so the price movement can be basically described as non-stationary AR(1) process with error e , or in other words random walk with drift.