## 4 Discussion
The improvements of increasing the noise model order were thus minimal compared to the cost of the increased complexity (i.e., more difficult to interpret, greater risk of overfitting and more computationally expensive), resulting in higher YIC values for third order noise models (Table 2). A [20] noise model showed the best balance between model fit and model complexity. BJ-TF models provided better fits than the exponential modelling methods. Whereas exponential models only provided an estimate of the general trend of the VO\({}_{2}\) response (Figure 2), BJ-TF models were able to account for the unwanted noise contributions around the general trend (Figure 5), without having to average VO\({}_{2}\) responses over several repetitions [21; 22]. These noise contributions are especially important for COPD patients, as the reduced VO\({}_{2}\) responses, due to the lower workloads that are feasible for COPD patients [3], increase the relative magnitude of the noise contributions (i.e., lower signal to noise ratio). Residual and autocorrelation plots confirmed that the noise models accounted for the most important noise contributions (Figure 3), and the remaining residuals were four times smaller than residuals from exponential models (Figure 5). Whereas exponential modelling models A and B failed to provide satisfying estimates of TD, BJ-TF models with a [20] noise model always provided satisfactory results without having to manipulate the data manually (cf. method C). The ability of BJ-TF models to separate the phase II contribution from other unwanted noise contributions ensured that these noise contributions could not influence the extracted kinetic feature values, which is a key advantage compared to exponential modelling. The influence of the unwanted contributions, mostly phase I, led to lower TD and higher TC, MRT, Amp and SSG values when applying methods A and B. Only method C produced similar feature values as BJ-TF models on a group level, pointing out that this method should be preferred over methods A and B when exponential models are applied on CORT data from COPD patients. Nevertheless, median absolute differences between the feature values of individual patients, as calculated with method C and BJ-TF models, were up to 24%, showing that different feature values were obtained for individual patients when the two different methods were applied. Unfortunately, due to the unwanted noise components in VO\({}_{2}\) responses, the true VO\({}_{2}\) kinetic feature values are never exactly known. As a result, no quantitative evidence could be provided that indicates which model (method C or BJ-TF) was mainly responsible for these differences in feature values on an individual level. Nevertheless, some theoretical considerations favour BJ-TF models over exponential models, as discussed below. Unwanted noise contributions influencing VO\({}_{2}\) kinetic features values are a general concern when applying exponential models [22; 23; 24]. In contrast, BJ-TF models explicitly account for the unwanted contributions and the extracted feature values will thus be less influenced by these contributions. Furthermore, parameters in the exponential models were estimated using the generally applied method of least squares, which can be influenced by unwanted noise contributions in the data, in contrast to the more robust refined instrumental variable approach that was used to estimate the model parameters in BJ-TF models [16; 25]. In addition, BJ-TF models do not require data manipulation by removing the first 20 s of data after the load onset. Although this method has been proven robust for changes in the amount of removed data under specific conditions, e.g., using the averaged data of four repetitions of the test and a sampling time of 10 s [26], the effect of changing the amount of removed data under less strict conditions, e.g., when only a single test is available, is still unclear and could thus influence the extracted feature values.