Addressing Non-stationarity with Stochastic Trend in the Context of Limited Time Series Data: An Experimental Survey

Stationarity in time series is a key property for practical data analysis, inferences, and predictions particularly in biosciences. Stationarity can be either deterministic or stochastic. If a time series data is not stationary, it can be rendered stationary through detrending or differentiation techniques. Differentiation can be performed in either an integer or fractional form. This paper investigates non-stationarity in time series data, focusing specifically on stochastic trends characterised by a unit root. It hypothesises that fractional differentiation can enhance forecast accuracy for datasets with limited volume. For experiments, 24 series corresponding to weekly Malaria and Typhoid Fever from Adamawa Region (Cameroon) are analysed and forecasted. Each series comprises 156 observations covering January 2021 to December 2023. After collecting, checking and classifying the data, four forecasting models, Auto Regressive Integrated Moving Average (ARIMA), Fractional ARIMA (ARFIMA), Long Short-Term Memory (LSTM), and the proposed Fractional Differencing and LSTM (FD-LSTM), are implemented. The models' performances are evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Coefficient of determination (R²) metrics, which inform further analysis and recommendations. Results reveal that ARFIMA outperformed the ARIMA by 93% in training and 100% in testing. Similarly, FD-LSTM achieved a 100% improvement over LSTM in training and testing. These findings underscore the value of achieving stationarity through fractional differentiation, enhancing model performance and providing a robust framework for forecasting in datasets with limited observations.