–19–
AR(1): a  vs.  MA(1): b  vs.  ARMA(1,1): a & b
¥ Check the effectiveness of GLSQ pre-whitening solution by examining pre-whitened residuals
H Pre-whitening: applying a linear transformation to the time series data to de-correlate the noise
oSymbolically, R-1/2 where R is the correlation matrix
¥ After pre-whitening, residuals (difference between data and fitted time series) should be (mostly) uncorrelated
¥ Power spectrum of white noise is flat
H Power spectrum = expected value of absolute value of Fourier transform, averaged over an infinity of repeated identical experiments
¥ Visually inspect graph of abs[FFT(pre-whitened residuals)]
H Should be flattish, with random excursions
oThis is noise, after all, and we donÕt have an infinity of data over which to average
¥ Next 4 slides:
H Graphs of ÒspectrumÓ for OLSQ and GLSQ using ARMA(1,1), AR(1), and MA(1) correlation models (generated using interactive AFNI, of course)
H For 3 strongly ÒactiveÓ voxels in one subject (block design: 30 s blocks; NIH 3T)
H Then the single subject activation maps for 6 types of analysis