# Hierarchical Modelling for CO\({}_{2}\) Variation Prediction for HVAC System Operation
## 1 Introduction  
The amount of energy consumed by buildings and industrial facilities accounts for around 70% of the total energy consumption in the US [1], and it constitutes a primary source of energy consumption in the majority of European countries [2]. Heating, Ventilation, and Air Conditioning (HVAC) systems represent a controllable energy consumer that fluctuates based on the thermal needs and occupants' comfort requirements [3]. Maintaining indoor air quality (IAQ) is an essential requirement for occupants due to the downstream effect of poor ventilation on the occupants' health [4]. An array of health-related problems arises with poor ventilation, such as decreased productivity [4, 5] and increased risks of COVID-19 infections [6, 7] which can reduce a human's quality of life [8]. Examples of these potential health-related hazards are encountered on a daily basis. Vehicle-based indoor contaminant levels increase in houses and buildings with indoor garages, increasing the risk of developing cancer and inducing fires [9, 10]. Moreover, households within industrial cities suffer from elevated levels of heavy metal contamination, which contributes to health-related problems [11]. In a similar context, [PERSON] et al. [12] uncovered a direct association between extended exposure to cooking oil fumes and deterioration in sleep quality. These dire consequences can be tackled with proper ventilation systems that provision fresh outdoor air to facilitate indoor air circulation [13]. The increased buildings' energy bills due to increased oil prices coupled with strict legislation to stifle Greenhouse Emissions (GHG) and the comfort needs of occupants are pushing the HVAC system operators to a critical juncture [14]. As a result, there is a need to match the occupants' comfort requirements while reducing the energy consumption of the HVAC systems by properly activating them. The demand-controlled ventilation (DCV) methods alter the ventilation systems based on the ventilation demands of the indoor environment. Since these demands are centred around the occupants' requirements, the prediction of the occupant's number changes is essential for controlling the ventilation loads. The regulatory bodies for efficient building development in North America and Europe [15] did not reach a consensus on concrete strategies or methods to utilize for measuring occupancy. In that regard, the literature and practical implementations suggest two main strategies [16]. The first method involves inferring the number of occupants by video surveillance cameras or the collection of occupants' identities, which raises some privacy concerns. The second method depends on proxy estimators of changes in occupancy using either motion and thermal energy sensors [17], Wi-Fi signals [18], or CO\({}_{2}\) levels [19], or a combination of sensors. The collection of ground truth data to reflect the number of occupants is infeasible in real time; thus, resorting to proxy estimators is a more practical approach with the already existing sensor infrastructure. In regard to proxy estimators, changes in occupancy can be estimated using Wi-Fi signals, CO\({}_{2}\) concentration level changes, and PassivelInfrared (PIR) sensors. However, employing Wi-Fi signals or activity levels to that end hinges on very loose assumptions. The Wi-Fi signals pre-suppose that occupants are connected to access points or hold a single device [20] while the PIR sensors are oblivious to static occupants and can potentially overestimate the number of occupants [21]. These factors favour CO\({}_{2}\) concentration changes that vary with the occupancy changes, which either stem from changes in their number or their activity, both with similar effects to the ventilation demands [22].The occupant's respiratory activity directly affects the indoor CO\({}_{2}\) concentrations, which highlights the distinctive property of CO\({}_{2}\) concentrations as a more accurate representation of occupancy changes.