Busso, Thierry, Pei-Ji Liang, and Peter A. Robbins. Breath-to-breath relationships between respiratory cycle variables in humans at fixed end-tidal PCO₂ and PO₂. J. Appl. Physiol. 81(5): 2287-2296, 1996.This study examined the statistical properties of breath-to-breath variations in the inspiratory and expiratory volumes and times during rest and light exercise. Sixty data sets were analyzed. Initial data and residuals after fitting time-series models were examined for 1) sustained periodicities with use of spectral analysis, 2) temporal changes in signal power with use of evolutionary spectral analysis, and 3) auto- and cross correlations with use of a portmanteau test. The major findings were as follows: 1) no sustained periodic components were detected; 2) temporal changes in signal power were normally present, but these did not affect significantly the results from time-series modeling; 3) for all variables, a simple autoregressive moving average (ARMA) AR₁MA₁ model generally described the autocorrelation; 4) considerable cross correlation remained between residuals from the AR₁MA₁ model; 5) relationships between variables could be described by using a multivariate time-series model; 6) residual fluctuations in end-tidal PCO₂ had little influence; and 7) responses were broadly similar between rest and exercise, although some quantitative differences were found. The multivariate model provides a description of the structure of the interrelationships between cycle variables in a quantitative and a qualitative form.