Searching for nonlinear relations in whitened jitter time series

Even in sustained vowels, durations of successive glottal cycles are not identical. They fluctuate quasi-randomly around an average. This phenomenon is known as jitter. More recently, correlation analysis has shown that perturbations of neighboring glottal cycles are interdependent, i.e. they are not purely random. We have shown that the non-random component of jitter can be modeled by means of a linear auto-regressive time series model which absorbs correlations between fluctuations of adjacent cycles and leaves a purely random component. The problem here is that nonlinear relations may be missed by correlation analysis or linear auto-regressive modeling. Nonlinear relations could be the signature of chaotic vibratory patterns which some authors expect for some pathological conditions of the vocal folds. We therefore decided to search inside whitened jitter time series (i.e. time series from which any linear correlations had been removed) for nonlinear or other anomalous dependencies between neighboring cycles. The results showed the following. Of the 265 time series, 231 appeared to have been correctly represented by linear auto-regressive models. For 29 series, out of the 34 remaining, deviations from pure randomness could be traced to isolated anomalous glottal cycles which statistical time series models had not taken into account. Finally, five signals, produced by three speakers, were detected which displayed relations between neighboring cycles which could not be traced either to linear correlations or to isolated glitches.