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/ . =================================================================
