New Criterion‎ For Fractal Parameter In Financial Time Series ‎

Since calculating the amount of fractal in the ARFIMA time series and increasing its ‎accuracy and bring it closer to reality is very important, this article intends to ‎investigate the possibility of modifying this computational formula by changing the ‎focus criterion and using simulation. In the present paper, by analysing and ‎simulating the fractal parameter for time series ARFIMA model and redefining and ‎reviewing the Fractal mathematical, a fractal calculus and dimension in ‎comparison ‎with Euclidean norms introduced. In this regard, first, a new criterion about fractal ‎or Hausdorff ‎component for measuring the forms of fractal time series introduced, ‎then the effects and functional ‎inquiries using simulation data searched, and some ‎mathematical proofs through simulation of ‎data achieved. The findings showed that, ‎the deviation of the new estimator from the simulated initial value is less, and closer ‎to reality as this new criterion introduced by changing the focus criterion and ‎replacing the mean with the median due to less sensitivity to out-dated data. The ‎new criterion is better for determining the fractal parameter and identifying its ‎degree of effectiveness. Finally, the findings empirically indicated that the proposed ‎criterion is more efficient and better ‎than the others for calculating fractal ‎dimensions.‎