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The purpose of this study was to provide a statistical description of the breath-to-breath variations in ventilation during steady breathing in both rest and during light exercise, with the end-tidal gases controlled by using an end-tidal forcing system. Sixty data sets were studied, only one of which was white (i.e., did not show autocorrelation). Three simple autoregressive moving average (ARMA) models, i.e., AR1, AR2, and AR1MA1, and one simple state-space model were fitted to the data and resulted in white residuals in 15, 31, 46, and 48 out of 60 occasions, respectively. Evolutionary spectral analysis revealed that only 13 data sets had a constant power spectrum, although 50 were uniformly modulated. An autoregressive estimate of variance could be used to "demodulate" the data in most cases, but the results were not significantly affected by fitting the model to the demodulated data. The results indicate that 1) both simple ARMA models and a simple state-space model can describe the autocorrelation present; 2) variations in spectral power were present in the data that cannot be described by these models; and 3) these variations were often due to a uniform modulation and did not significantly affect the coefficients for the models. For these kinds of data, a heteroscedastic form of state-space model provides an attractive theoretical structure for the noise processes.

Original publication




Journal article


J Appl Physiol (1985)

Publication Date





2274 - 2286


Air Pressure, Carbon Dioxide, Data Interpretation, Statistical, Exercise, Humans, Models, Biological, Oxygen Consumption, Respiratory Mechanics, Rest, Stochastic Processes