[EMAIL PROTECTED] (Pradyumna S Upadrashta) wrote in message news:<[EMAIL PROTECTED]>... > If one applies a linear filter, with a lowpass of 400Hz, is it possible > for it to induce spurious autocorrelation (that persists essentially > what seems like 'forever') in a time-series? > > I'm examining a time-series which was recorded from an empty shielded > room (the sensors detect very minute magnetic fields on the order of > femtoTesla), so it should consist of sensor noise + environmental noise. > However, upon inspection of the power spectrum, I notice a roll-off > behavior ~400Hz (orig sampling rate was 1017Hz) and the ACF and PACF > display very odd behavior as mentioned. Our data acquisition person > insists that a standard low-pass filter was used, with a DC offset. If > this is the case, then i'm unable to understand why a time-series that > should be pure white noise, isn't... I don't want to jump on the idea > that it is nonlinear without sufficient justification for doing so. > > I'm not sure if these results are due to some inherent nonlinearities in > the signal, or whether the filter could have induced these behaviors? If > the filter was nonlinear, then I speculate that it could explain the > signal structure i'm seeing? I have often heard of long autocorrelation > times being associated with nonlinear structure (e.g., Kantz and > Schreiber, 1997 "Nonlinear Time Series Analysis") > > Also, what is the reasonable thing to do, with regard to measuring > autocorrelation functions, for a time-series that appears non-stationary > locally (say on plots of a few 1000 ms duration), but doesn't exhibit > significant drift in the long run (on plots of 5000 ms duration)? That > is, when can we declare a time-series to be 'stationary' in the > wide-sense? Can we declare it to be non-stationary, if at large > time-scales it appears to be relatively stable? Is it enough if a plot > is visually stationary? > > The caveat of not being able to 'know for sure' when something is > stationary a priori, is that one can't rely on the power spectrum since > it assumes a stationary signal structure for its estimation! (or am I > wrong about this?) > > I suppose one could look for stationary segments of the signal, and then > attempt to compare spectra across multiple 'stationary looking' > segments; if the signal really is stationary, i'd expect no changes > right? I have 45,000 data points in a single time-series. > > What is the most correct test for non-stationarity which doesn't rely on > any assumptions? Also, if what i've done is correct, then how do I > interpret the ACF and PACF functions i've described? > > Any help would be greatly appreciated! > > thanks in advance... > p > > _____________________________________ > Pradyumna Sribharga Upadrashta, PhD Student > Scientific Computation, UofMN > > . > . > ================================================================= > Instructions for joining and leaving this list, remarks about the > problem of INAPPROPRIATE MESSAGES, and archives are available at: > . http://jse.stat.ncsu.edu/ . > =================================================================
P. It is always possible to inject structure by using an incorrect filter . For example if you difference a white noise process you create a series that has an autocorrelation function that goes on forever. This is why you only use filters that are required. You should also know that changes in level in a series can cause the ACF to go on forever, so to speak .This also applies to trend changes. I don't rally know but I suspect that unnecessary power transformations such as logs, reciprocals, arc-sine , square root et.al. my also have an effect on the ACF. Regards Dave Reilly AUTOMATIC FORECASTING SYSTEMS http://www.autobox.com . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
