Pradyumna S Upadrashta wrote: > Hi, > > 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? > > P >
Ref: Jones DA (1976) Nonlinear autoregressive processes. Proc Roy Soc Lond A v360 71-95 This paper contains an example of a nonlinear process (1-step dependent) where the autocorrelations are found exactly and shown not to match those of a linear AR(1) process. This might be thought to relate to your question. However, non-linearity and length of autocorrelation are not directly related. It is well-known that you can construct a linear process with essentially any (valid) autocorrelation function you like, so non-linearity isn't necessary for long acf's. There may be an argument about "simple structures". If you demand that a model should have a simple structure (however you might judge this), then maybe you do need to resort to a simple non-linear structure to get a long acf. But "simple structure" shouldn't be confused with a structure you are familiar with, as in ARMA models, where FARMA are known for their ability to give long acfs. I don't understand "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?" ... ....long acfs are not necessarily non-stationary ....nonlinear processes are not necessarily non-stationary David Jones . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
