"Pradyumna S Upadrashta" <[EMAIL PROTECTED]> wrote: > Are there any dynamical folks who speak statistics well enough that you > can clarify what is meant by "nonlinear correlation"? are there any > statisticians who can give me the correct way to think about correlation > structure in a time-series, and how "nonlinear correlations" could > affect a process (besides leading to some form of nonstationarity)?
Try exploring around http://www.mpipks-dresden.mpg.de/~tisean You have to drop the linear-specific notion of 'correlation', and adopt a more general notion of prediction error (correlation is the reduction in prediction error using a linear univariate model, where the prediction error is measured as the percentage of variance explained). It turns out that you can predict pretty well in some cases by using a nonlinear method of nearest neighbors. Imagine that you notice that the time series has been behaving a little like once in the past: you then predict directly from the matching history. Let me illustrate this with a text series: If you saw me say blah, did I say .... [We notice that "say " was followed by "blah" in the past, so we predict "blah", and we compute the prediction error.] Aleks . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
