long memory

This paper explores multifractal analysis for the selected time series water pollution data set and further prediction based on BOD measure with ARFIMA-based fractal model. MFDFA multifractal algorithm is applied for estimating the fractal differentiation parameter of the ARFIMA. The obtained results are compared with similar obtained with autoregressive ARIMA model and basic ARFIMA fractal model. The study reveals an enhancement in accuracy with the use of combination of multifractal analysis and fractal methods for water pollution prediction

The work created software and algorithmic support for modeling and forecasting the Bitcoin cryptocurrency using the ARFIMA (AutoRegressive Fractionally Integrated Moving Average) fractal model. Time series forecasting models (autoregressive, fractal) were analyzed. The selection of the most appropriate parameters of the selected fractal model was also carried out to maximize accuracy in view of the RMSE metric. The series were analyzed for trend, seasonality, white noise, non-stationarity and long-term memory.