Forecasting NHS Emergency Demand: A Box-Jenkins ARIMA Approach to A&E Capacity Planning

References

[1] Bouderhem, R. (2024) ‘Shaping the future of AI in healthcare through ethics and governance’, Humanities and Social Sciences Communications, 11, p. 416.

[2] Box, G.E.P. and Jenkins, G.M. (1976) Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day.

[3] Farimani, R.M., et al. (2024) ‘Models to predict length of stay in the emergency department: a systematic literature review and appraisal’, BMC Emergency Medicine, 24(1), p. 54.

[4] GOV.UK (2025) Faster treatments and support for health workers as AI tackles A&E bottlenecks. Department for Science, Innovation and Technology. Available at: https://www.gov.uk/government/news/faster-treatments-and-support-for-health-workers-as-ai-tackles-ae-bottlenecks

[5] Health Foundation (2025) Did the NHS experience record pressures this winter? Available at: https://www.health.org.uk/reports-and-analysis/analysis/did-the-nhs-experience-record-pressures-this-winter

[6] House of Commons Library (2024) NHS readiness for winter 2024/25. Available at: https://commonslibrary.parliament.uk/research-briefings/cdp-2024-0139/

[7] Hyndman, R.J. and Athanasopoulos, G. (2021) Forecasting: Principles and Practice. 3rd edn. Melbourne: OTexts.

[8] Kolambe, M. and Arora, S. (2024) ‘Forecasting the future: a comprehensive review of time series prediction techniques’, Journal of Electrical Systems, 20(2s), pp. 575–586.

[9] Kontopoulou, V.I., Panagopoulos, A.D., Kakkos, I. and Matsopoulos, G.K. (2023) ‘A review of ARIMA vs. machine learning approaches for time series forecasting in data driven networks’, Future Internet, 15(8), p. 255.

[10] Morbey, R.A., Todkill, D., Moura, P., Tollinton, L., Charlett, A., Watson, C. and Elliot, A.J. (2025) ‘Using machine learning to forecast peak health care service demand in real-time during the 2022–23 winter season: a pilot in England, UK’, PLOS ONE, 20(1), e0292829.

[11] NHS England (2026) A&E Attendances and Emergency Admissions: Quarterly Time Series [dataset]. Available at: https://www.england.nhs.uk/statistics/statistical-work-areas/ae-waiting-times-and-activity/

[12] Pham, T. (2025) ‘Ethical and legal considerations in healthcare AI: innovation and policy for safe and fair use’, Royal Society Open Science, 12(5), p. 241873.

[13] Poursoltan, L., et al. (2025) ‘Prospective comparison of econometric, machine learning, and foundation models for forecasting emergency department boarding patients’, npj Health Systems, 2(1), p. 49.

[14] Silva, E., Pereira, M.F., Vieira, J.T., Ferreira-Coimbra, J., Henriques, M. and Rodrigues, N.F. (2023) ‘Predicting hospital emergency department visits accurately: a systematic review’, International Journal of Health Planning and Management, 38(4), pp. 904–917.

[15] Tuominen, J., Lomio, F., Oksala, N., Palomäki, A., Peltonen, J., Huttunen, H. and Roine, A. (2022) ‘Forecasting daily emergency department arrivals using high-dimensional multivariate data: a feature selection approach’, BMC Medical Informatics and Decision Making, 22, p. 121.

[16] Vollmer, M.A., Glampson, B., Mellan, T., Mishra, S., Mercuri, L., Costello, C., Klaber, R., Cooke, G., Flaxman, S. and Bhatt, S. (2021) ‘A unified machine learning approach to time series forecasting applied to demand at emergency departments’, BMC Emergency Medicine, 21(1), pp. 1–14.

@article{1722770,
      author = {Precious Ejiba, Efemena Ikpro},
      title = {Forecasting NHS Emergency Demand: A Box-Jenkins ARIMA Approach to A&E Capacity Planning},
      journal = {Iconic Research And Engineering Journals},
      year = {2026},
      volume = {10},
      number = {3},
      pages = {27-39},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1722770.pdf},
      abstract = {Accurate short-to-medium-term forecasting of Accident & Emergency (A&E) attendance demand is a precondition for safe capacity planning across the National Health Service (NHS), where staffing, bed allocation, and escalation decisions are made against a constitutional four-hour treatment standard that the system has not met since 2014-15. This study applies a Box-Jenkins ARIMA methodology, benchmarked against Holt’s Linear Exponential Smoothing (LES), to 61 quarters (2011-12 Q1 to 2026-27 Q1) of NHS England quarterly total A&E attendance data. The series is confirmed non-stationary in levels (Augmented Dickey-Fuller statistic = -1.74) and stationary after first differencing (ADF = -4.56). Autocorrelation and partial autocorrelation analysis of the differenced series identifies a single significant lag-1 term consistent with an IMA(1,1) signature. An ARIMA(0,1,1) specification is selected over higher-order alternatives on an eight-quarter holdout backtest (RMSE = 154,563; MAE = 127,861; MAPE = 1.86%), outperforming both Holt’s LES (MAPE = 2.22%) and a more heavily parameterised ARIMA(2,1,2) that achieves marginally better in-sample information criteria but materially worse out-of-sample accuracy (MAPE = 3.59%) which is a concrete demonstration of in-sample overfitting. Ljung-Box diagnostics confirm residual white noise at all tested lags. The selected model projects total quarterly attendances rising from approximately 7.18 million in 2026-27 Q2 to 7.72 million by 2031-32 Q1 (+7.5%), with a 95% prediction interval that widens from ±905,000 to ±5.33 million over the five-year horizon, a finding with direct implications for how far ahead NHS planners can responsibly commit capacity decisions to a single point forecast. The paper closes with recommendations for NHS operational planning teams and for healthcare data science practice more broadly.},
      keywords = {ARIMA; Box-Jenkins methodology; exponential smoothing; healthcare demand forecasting; NHS A&E attendances; capacity planning; forecast uncertainty.},
      month = {September},
      doi = {https://doi.org/10.64388/IREV10I3-1722770}
  }