PowerPoint Presentation - Serial Correlation in AFNI

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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 don’t have an infinity of data over which to average

• Next 4 slides:

H Graphs of “spectrum” 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 “active” voxels in one subject (block design: 30 s blocks; NIH 3T)

H Then the single subject activation maps for 6 types of analysis