Home / Current Issue / Paper 1722770
Forecasting NHS Emergency Demand: A Box-Jenkins ARIMA Approach to A&E Capacity Planning
Subject area: Science,Engineering and Technology · Area of research: Data Science and Analytics
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.
How to cite this paper
@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},
}