Thanks for the suggestions. I will try to contact Prof. Churvich. My other question pertains to conflicting ideas with regard to the measure of correlation.
The time-series folks recognize a correlation to be a linear 'fit' between two (or more) variables, while they recognize the idea of a "nonlinear relationship" between two variables, they don't seem to appreciate the term "nonlinear correlations" being used to described the case when the relationship is "nonlinear" (for example when inspecting a lagplot). The dynamics community often refer to "nonlinear correlations", are they simply referring to correlations in which the relationship is nonlinear? Are they both saying the same thing, but just won't admit it to one another? Or am I not grasping the idea? 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)? I just need better intuition and definition for these terms. much appreciated, pradyumna _____________________________________ Pradyumna Sribharga Upadrashta, PhD Student Scientific Computation, UofMN >-----Original Message----- >From: [EMAIL PROTECTED] >[mailto:[EMAIL PROTECTED] On Behalf Of David Reilly >Sent: Sunday, September 28, 2003 7:40 PM >To: [EMAIL PROTECTED] >Subject: Re: [edstat] stationarity, time-series analysis, >power spectra, etc > > >[EMAIL PROTECTED] (David Reilly) wrote in message >news:<[EMAIL PROTECTED]>... >> [EMAIL PROTECTED] (Pradyumna S Upadrashta) wrote in message >> news:<[EMAIL PROTECTED]>... >> > Hi Dave, >> > >> > I suspected that this was the case. I did a simple >simulation using >> > normal random numbers, rescaled using a log-transform; indeed, the >> > acf shows significant peaks that go on 'forever'. I suspect that a >> > nonstationarity in the original time-series is the cause of the >> > behavior I see, yet, if the process is nonlinear, then I can't >> > justify elminating the nonstationarity which might destroy the (if >> > any) nonlinear dynamics of the process that i'm interested in. I'm >> > somewhat stuck on what to do here. >> > >> > What is considered a reasonable procedure for examining this >> > time-series and determining whether it contains nonlinear >structure? >> > that is, what types of linear analysis should I undertake before >> > trying to look at nonlinearity. I realize that one could >follow the >> > ARIMA approach and attempt to model trends, seasonality, take >> > differences, etc and then fit an ARMA model to the resultant >> > stationary process, but if we are interested in the nonlinear >> > structure, would this still be the correct approach? >> > >> > Any suggestions are appreciated. A recipe for initial analysis is >> > even more appreciated. >> > >> > regards, >> > P >> > >> > _____________________________________ >> > Pradyumna Sribharga Upadrashta, PhD Student >> > Scientific Computation, UofMN >> > >> Prady, >> >> I myself have not done too much in this area. You might consider >> reviewing >> >> >> http://pages.stern.nyu.edu/~churvich/TimeSeries/Handouts/NonLin.pdf >> >> and contacting Prof. Stern at NYU . >> >> You might also consider simulating some non-linear models and then >> study the implications of pre-filtering with identified ( albeit >> incorrectly ) ARIMA structure. I would extend the simulation to >> include various deterministic structures such as local time >trends and >> stochastic structures such as differencing with a trend which often >> masquerades as a linear time trend model. >> >> Hope this helps ... >> >> Dave Reilly >> AUTOMATIC FORECASTING SYSTEMS >> http://www.autobox.com > > > >oops ... that might be Prof Churvich at the Stern School of >Business NYU .. > > >dave r >. >. ================================================================= >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/ . =================================================================
