## 1 Introduction  
Chronic obstructive pulmonary disease (COPD) is a common lung disease characterised by persistent airflow limitations due to a combination of airway and alveolar abnormalities. COPD is associated with high morbidity and mortality rates, posing a high economical and societal burden [1]. The most important symptom of COPD is dyspnoea during daily activities, but later also at rest. As a result, patients become physically less active, which is the start of a vicious circle of physical deconditioning [2]. Physical capacities can be assessed using standard exercise tests like a cardiopulmonary-nonary exercise test (CPET, incremental cycling load) or a constant work rate test (CWRT, constant cycling load) [3]. During a CPET, oxygen uptake (VO\({}_{2}\), ml.min\({}^{-1}\)) increases linearly until the maximal or peak VO\({}_{2}\) value is reached. This maximal (or peak) VO\({}_{2}\) value, the maximal load reached during CPET and the endurance time during CWRT are the most frequently used metrics for evaluating physical capacities. However, there is additional information, besides these maximal values, that can be extracted from the breath-by-breath VO\({}_{2}\) time series that are generated during these tests. During a CWRT, there is typically a 3-phase VO\({}_{2}\) response towards the step increase of cycling load (W). During phase I, the cardiodynamic phase, VO\({}_{2}\) shows an instant response driven by an increased cardiac output and pulmonary blood flow (Figure 1). In phase II, the primary component of the response, VO\({}_{2}\) increases exponentially, similar to the working muscle oxygen uptake. In phase III, VO\({}_{2}\) can reach a steady-state or can steadily keep increasing, i.e., VO\({}_{2}\) slow component (Figure 1), depending on the exercise intensity [4]. Kinetic analyses of the VO\({}_{2}\) response aim to quantify the speed and amplitude of the primary (phase II) response using a combination of features. Time delay (TD), time constant (TC) and mean response time (MRT = TD + TC) assess the speed of the response. Response amplitude (Amp) and steady state gain (SSG = Amp.\(\Delta\)W\({}^{-1}\)) assess the magnitude of the response, with \(\Delta\)W indicating the step increase of cycling load at the start of the exercise test (Figure 1). These features quantify the ability to respond to the increased physical load during a CWRT [4]. Generally, COPD patients exhibit a slower VO\({}_{2}\) response than healthy subjects [5; 6], but supplemental oxygen [7], medication use [8; 9] and exercise training [10], can speed up the VO\({}_{2}\) response to the step increase in cycling load. Typically, exponential models are used to extract these kinetic features from the VO\({}_{2}\) time series. Three mono-exponential modelling methods have been described in COPD literature, which will be referred to as method A [6; 8], B [10; 11] and C [9; 12]. Method A assumes there is no delay in the VO\({}_{2}\) response (TD = 0 s), whereas methods B and C estimate a TD value as one of the model parameters. Method B uses data starting from t = 0 s (load onset), while method C aims to exclude the contribution of the cardiodynamic phase by only using data starting from t = 20 s. Nevertheless, these exponential models are all still influenced by other unwanted noise contributions, such as measurement noise or cardiac output dynamics that are not related to the increased working muscle oxygen uptake. In contrast to the generally applied exponential models, Box-Jenkins transfer function (BJ-TF) models can extract the same kinetic features [13] without being affected by these unwanted noise contributions. BJ-TF models are able to separate the unwanted contributions from the noise-free primary VO\({}_{2}\) response (i.e., phase II). Therefore, extraction of the kinetic features will not be influenced by the unwanted contribution of these additional components, and will only reflect the working muscle oxygen uptake. To the authors' knowledge, BJ-TF models have not yet been used to extract kinetic features from CWRT data.