Oscillometry is a useful measure of lung function and recently has been used to estimate temporal variation in physiological mechanical properties of the lung, but to date, analysis methods assume stationarity or short-time stationarity despite substantial temporal variation, particularly in disease. The effect of time-varying parameters on the accuracy of estimates of impedance has not been previously analyzed. In this paper we analytically, computationally, and with added experimental data from seven children with asthma, assess the time-frequency transfer function of the time-varying respiratory system. We then evaluate the accuracy in determining the time-varying parameters of respiratory impedance. We introduce, for the first time, the error arising from respiratory time variation, termed the time-varying error (TVE) and demonstrate how TVE unexpectedly increases with increasing breathing rate independent of breathing noise amplitude. For breathing rates less than 0.4 Hz, we found that common analysis methods could be moderately accurate with less than 5% error. Since tracking time-varying impedance shows strong potential for assessing the severity of respiratory disease, it is import to recognize that errors should be avoided, or compensation circuits and systems developed based on the TVE, particularly important in patients with high variation or breathing rate such as children and infants.