## 1 Introduction  
Across the world, healthcare systems are under stress and this has been hugely exacerbated by the COVID pandemic. Key Performance Indicators (KPIs), usually in the form of time-series data, are used to help manage that stress. Making reliable predictions of these indicators, particularly for emergency departments (ED), can help to identify pressure points in advance and also allows for scenario planning, for example, to optimise staff shifts and planning escalation actions. According to Medway Foundation Trust (MFT), where the results of this study are applied, it is important to accurately forecast after exceptional events in their data, such as the pandemic, because forecasts are of increased importance at these critical moments. When the uncertainty level is greater, correct predictions may benefit their decision making more than usual (although models must also perform well in non-exceptional circumstances). When analysing the healthcare systems, great significance has been placed on predicting patient arrivals in acute units, and in particular emergency department (ED) attendances and throughput. Typically, patients arrive at irregular intervals, often beyond the control of the hospital, and arrivals show strong seasonal and stochastic fluctuations driven by factors such as weather, disease outbreaks, day of the week and socio-demographiceffects [1]. Accordingly, researchers use a variety of methods to predict ED visits over various periodic intervals, e.g., [2; 3]. Furthermore, predicting KPIs in EDs can depend on several factors, e.g., [4; 5]. Typically, EDs deal with a variety of life-threatening emergencies, arising from causes such as car accidents, disease, pollution, work-place hazards, aging, changing population, pandemics and many other sources. However, multivariate models usually consider only a small number of dependent/independent variables out of numerous possibilities, and in ED that can result in dangerous omissions. For example, variables that are not captured (especially those with high correlations, multi-variable correlation lags and high levels of noise) may drive multi-variate predictions of captured variables in the wrong direction [6]. For predictions of this type, a common approach is to auto-correlate the data. Since all the numerous variables have been an influence on the past values of the time-series under investigation, prediction models can use these data as a baseline to calculate future time-series values. Apart from this baseline, other variables, both dependent and independent, and represented by other indicators, may be included in the model by considering the covariance between them. Accurate and reliable forecasts of various types of indicator can help to efficiently allocate key healthcare resources, including staff, equipment and vehicles, when and where they are most needed [2], and avoid allocating them at non-critical periods. This justifies considerable efforts to make reliable and accurate predictions of ED data to help hospital managers in making decisions about how to meet the expected healthcare demand effectively and in a timely fashion [1]. As a linear model, ARIMA can typically capture linear patterns in a time series efficiently, and so many studies adopt it either to evaluate relationships between variables, or use ARIMA forecasts as a benchmark against which to test the effectiveness of other models, e.g., [7]. This has been applied to ED data previously and as examples, [PERSON] et al. [3], [PERSON] et al. [8], and [PERSON] [9] have developed ARIMA models for forecasting hospital ED attendances and have verified the fitness of ARIMA, in that context, as a readily available tool for predicting ED workload. In particular, [PERSON] [9] used ARIMA to forecast yearly patient attendances at EDs in the Trent region of the UK and found that the forecast for attendances was just 3 per cent away from the actual figure. Meanwhile, [PERSON] et al.