Multifractal Analysis and ARFIMA Modeling in Predicting Organic Pollution of the Danube River

This paper presents an investigation into the complex dynamics and enhanced predictability of organic water pollution using a multifractal methodology. The study utilizes a time series dataset of water pollution measures, where time-series analysis and the Multi-Fractal Detrended Fluctuation Analysis (MFDFA) were individually applied to both Biochemical Oxygen Demand (BOD) and Chemical Oxygen Demand (COD) metrics. By analyzing and comparing the characteristics of each metric, the research establishes a deeper insight into the overall organic pollution dynamics, which informs the subsequent modeling. The MFDFA results were used to accurately estimate the fractal differentiation parameter (d) for the ARFIMA (AutoRegressive Fractionally Integrated Moving Average) model. The resulting forecasts for pollution were evaluated and compared against those obtained from the traditional ARIMA (AutoRegressive Integrated Moving Average) model and a basic ARFIMA fractal model. Comparative analysis, utilizing performance metrics such as Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE), conclusively demonstrates that the methodology integrating multifractal analysis and the ARFIMA fractal model provides an enhancement in predictive accuracy for water pollution time series for metrics where high multifractal evidence was detected through the MFDFA, thereby validating the utility of fractal methods in capturing the underlying complexity and long-memory dependencies of highly heterogeneous environmental processes.