Given the two responses provided, I believe my confusion is cleared up. I probably read too strongly into the statement about nonlinearity and ACF being related.
I will have a look at that reference as it sounds quite relevant. thanks! p _____________________________________ Pradyumna Sribharga Upadrashta, PhD Student Scientific Computation, UofMN >-----Original Message----- >From: [EMAIL PROTECTED] >[mailto:[EMAIL PROTECTED] On Behalf Of Radford Neal >Sent: Monday, October 06, 2003 12:46 PM >To: [EMAIL PROTECTED] >Subject: Re: [edstat] nonlinearity and autocorrelation times > > >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/ . >================================================================= > . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
