Pradyumna S Upadrashta <[EMAIL PROTECTED]> wrote: >Does anyone know of any (simple) papers that discuss the relationship >between nonlinearity and long-autocorrelation times in time-series? Many >times I have run across the suggestion that "long autocorrelation times" >suggest nonlinear behavior, but aside from the clearly non-stationarity >of such processes, what else can be said about long autocorrelation >times?
I'm not particularly familiar with this area, and can't give you any references, but I have a couple comments. First, a time series with long autocorrelation times must be stationary. Autocorrelation time isn't defined for non-stationary series. Of course, a non-stationary series will often produce *estimates* for autocorrelations that appear to correspond to a time series with long autocorrelation time, but these are estimates for something that doesn't actually exist. Second, I don't see why long autocorrelation times would have any particular relationship with nonlinearity - assuming that by the latter, you mean a non-Gaussian joint distribution. There is a multivariate Gaussian distribution with any given correlation matrix. There will also, of course, be many non-Gaussian distributions with the same correlation matrix. Radford Neal ---------------------------------------------------------------------------- Radford M. Neal [EMAIL PROTECTED] Dept. of Statistics and Dept. of Computer Science [EMAIL PROTECTED] University of Toronto http://www.cs.utoronto.ca/~radford ---------------------------------------------------------------------------- . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
