Robust Prediction of Healthcare Inflation Rate With Statistical and AI Methods in Iran

The expected healthcare (HC) inflation rate (IR) (HCIR) is an important variable for all economic agents within HC systems. In recent years, during the COVID-19 pandemic, Iran has experienced a high HCIR in its health system. In this context, a robust approximation of HCIR will be a helpful tool for health authorities and other decision makers. Using monthly time series data of HCIR in Iran, we developed various forecasting techniques based on classical smoothing methods, decomposition ETS (error, trend, and seasonality) approaches, autoregressive (AR) integrated moving average (ARIMA), seasonal ARIMA (SARIMA), and a multilayer nonlinear AR artificial neural network (NARANN) with several training algorithms including Bayesian regularization (BR), Levenberg–Marquardt (LM), scaled conjugate gradient (SCG), Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton, conjugate gradient with Powell–Beale restarts (CGB), conjugate gradient with Fletcher–Reeves updates (CGF), and resilient propagation (RPROP) algorithms. Initially, based upon various criteria and possible combinations, we selected the superior model for each method separately. After that, the best model in each category is involved in 6- and 12-multi-step-ahead prediction. In this stage, several error criteria are calculated. According to our findings, in a six-step forecasting window, the Holt–Winters with a multiplicative seasonal pattern and SARIMA showed less bias, though compared to other alternatives like NARANN-lm/br, the difference was relatively small. In the next process, by doubling the forecasting window, it is observed that artificial neural network (ANN) (i.e., Bayesian NARANN) strictly outperformed other models. As a result, in shorter steps, the Holt–Winters method can provide a better prediction, while in longer windows, Bayesian NARANN can be implemented vigorously for the prediction. Finally, we used 10 models to predict the future trend of HCIR in Iran till the end of July 2024.