New Criterion‎ For Fractal Parameter In Financial Time Series ‎

Advances in Mathematical Finance and Applications

مقاله 13، دوره 7، شماره 4، دی 2022، صفحه 1025-1043   

نوع مقاله: َApplied-Research Paper

شناسه دیجیتال (DOI): 10.22034/amfa.2021.1917040.1527

نویسندگان

Mehrzad Alijani¹؛ bahman banimahd^{* 2}؛ Ahmad Yaghobnezhad³

¹Department of Management and Economics, Science and Research Branch, Islamic Azad University, Tehran, Iran

²Associate Professor in Accounting, Head of Accounting Department, Islamic Azad University- Karaj Branch, Iran

³Department of Economic and Accounting, Islamic Azad University of Central Tehran Branch, Tehran, ‎Iran ‎

چکیده

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.‎

کلیدواژه‌ها

Fractal Dimension؛ Hausdorff measure؛ ARFIMA time series؛ Simulation؛ ‎R

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