On Sat, 2003-09-27 at 15:00, Pradyumna S Upadrashta wrote: > 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?
Was the filter a real-time filter (analog or digital), or was it a frequency-domain filter applied after the fact? The effect you describe is how most linear filters work, in practice; the real-time ones are called "recursive". Another name for them is "infinite impulse response" filters (that should give you a hint). ... > 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. That's only 100 Hz you've got until you hit the Nyquist frequency (which I'm sure you know). Data near the Nyquist frequency, and near 0 Hz, are both a bit biased if you're using an FFT anyway (are you using the fftw libraries? they're quite nice for this). > 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... See above. > 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?) You are. Read Bloomfield's introduction, with the notion of "detrending" the raw data. > 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. See detrending. Cheers Jason -- Indigo Industrial Controls Ltd. http://www.indigoindustrial.co.nz +64-(0)21-343-545 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
