Numerical research of persistent time series based on the ARFIMA model
The work is devoted to methods for detecting long-term memory in financial time series. Using the method of analysis with the help of the original program code, a number of values of the real financial index S & P500 were studied, estimates of the Hurst index were obtained, and persistence was demonstrated. To solve the problem of predicting the future values of a series, the ARFIMA model is proposed, which is a generalization of the standard ARIMA model and involves the use of a fractional differentiation operator. A two-stage algorithm for constructing a forecast for a series of logarithmic profits is presented and implemented. It is shown that the use of the ARFIMA model improves the quality of the forecast in comparison with ARIMA for all standard metrics.