A while back I decided to look up some of the more academic methods and models used to conduct analysis on financial time series data. I saw the progression in linear statistical tools going from correlation, to ARMA, to ARIMA, and then to GARCH---and then found out implied volatility is probably as effective as GARCH at its best. It all seemed a lot of work for very little when there are shortcuts available that can do the trick for far less mental expenditure. Still I took note of nonlinear methods being discussed as the next frontier but didn't really look into it. My question now is what does it mean when one talks of nonlinear trading analysis? Is this principally about neural networks? Something else? What? Thank you for any explanation that you give.

http://en.wikipedia.org/wiki/Nonlinear Most of the methods you mentioned (ARMA, etc.) are based on the assumption of stationarity, which is related to linearity, and it is now well established that financial time series are nonstationary. So the hope is that nonlinear methods will be more capable of analyzing such time series than traditional linear methods.

So are you saying nonlinear methods in the main generally try to model changes in skedasticity and stationarity on top of the linear aspect? What are the frequent tools used in such analysis and modelling?

Thanks for the link. I think may have even seen that textbook referred to previously when it was newly published. I assume to make use of these techniques requires specialized statistical software? MatLab, S, and the like? I think I abandoned this line of research when I figured out I didn't have and was unfamiliar with any of the tools available to use it. Can any of the common charting programs out there can handle it or is that a fat chance? If you use these ideas what software do you use to implement them?

..require an understanding of Calculus (remember that?) and Differential Equations. Much of my work involves developing specialized tools to describe the chart images in specific mathematical terms.. collecting the different patterns (a model describes a patten) into a System of Models.. then trading that system. Much of the work is tedious.. one cannot assume "pretty" mathematical relationships derived from "classical" differential equation analysis. So.. many "experiments" involving these new tools are conducted, then applying those models that pass muster to actual markets. I currently use only TradeStation Software to define and apply these customized tools. It is VERY FLLEXIBLE. Your IMAGINATION is your only limitation!!! Mh

Well when you put it like that I guess I see some ways some ideas can be applied in regular charting programs. Still, correct me if I'm wrong, but a system based on a differential equation can be something as simple as one using MACD. Also what are ideas for dealing with nonstationarity and heteroskedasticity? Can one address that by simply using a volatility indicator as a filter?