Addressing non-stationarity with stochastic trend in the context of limited time series data: An experimental survey in healthcare analytics

Stationarity is a fundamental assumption in time series modeling that underlies reliable statistical inference and forecasting. Time series data can be found in many domains, including industry, engineering, finance, economics, epidemiology, and health care analysis. This study addresses stochastic non-stationarity arising from unit root processes. It explores the efficacy of fractional differentiation as a means of achieving stationarity, especially in the context of limited-sample time series data, and attempts to confirm it statistically through experiments. To this end, 24 series of malaria and typhoid incidence were used, from the Adamawa region of Cameroon, collected weekly from January 2021 to December 2023, 14 of which were non-stationary. Four models were tested: Autoregressive Integrated Moving Average (ARIMA), Fractional ARIMA (ARFIMA), Long Short-Term Memory (LSTM), and a hybrid Fractionally-Differentiated-LSTM (FD-LSTM) proposed in this paper. The accuracy of the prediction models was assessed by the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Coefficient of Determination (R²) values. The results show that the Pearson correlations between the original time series and the integer-differentiated series are weak, mainly between 0.2 and 0.4, while they are between 0.75 and 0.98 for the fractional-differentiated series. Moreover, ARFIMA outperforms ARIMA by 93% in training and 100% in testing, while FD-LSTM achieves a 100% improvement over the standard LSTM model. These results contribute to the methodological toolkit for time series forecasting in data analytics and highlight the statistical and practical advantages of fractional differencing in small sample preprocessing.