ارزيابي و بررسي خاصيت فراكتالي بازارهاي سرمايه برپايه تحليل نوسانات روند زدايي شده (مورد مطالعه: بازار ارز و شاخص بورس تهران)

Evaluating and study of the Fractal Properties of Capital Markets Based on DE trended Fluctuation Analysis (Case Study: Exchange Market and Stock Index of Tehran)

در اﯾﻦ ﺗﺤﻘﯿﻖ ﺣﺎﻓﻈﻪ ﺑﻠﻨﺪﻣﺪت ﺷﺎﺧﺺ ﺑﻮرس و ﻧﺮخ ارز )دﻻر( ﺑﺎ اﺳﺘﻔﺎده از ﺗﺤﻠﯿﻞ ﻧﻮﺳﺎﻧﺎت روﻧﺪزداﯾﯽ ﺷﺪه ﻣﻮرد ﺑﺮآورد ﻗﺮار ﮔﺮﻓﺖ. ﺑﻪ ﻣﻨﻈﻮر روﻧﺪزداﯾﯽ داده ﻫﺎ، روﯾﮑﺮد ﮔﺎرچ ﭘﯿﺸﻨﻬﺎد ﺷﺪ و اﻟﮕﻮي ﺑﺮآورد ﺣﺎﻓﻈﻪ ﺑﻠﻨﺪﻣﺪت ﺑﺮاي ﻫﺮ دو روش ﻣﺘﺪاول و ﮔﺎرچ ﺑﻪ ﻃﻮر ﺟﺪاﮔﺎﻧﻪ اﺟﺮا ﺷﺪ. ﺑﺮاي اﯾﻦ ﻣﻨﻈﻮر از داده ﻫﺎي روزاﻧﻪ ﺷﺎﺧﺺ ﺑﻮرس و ﻧﺮخ دﻻر در ﺑﺎزار آزاد ﻃﯽ دوره 1393/01/05 ﺗﺎ 1399/11/19 اﺳﺘﻔﺎده ﺷﺪ. ﻧﺘﺎﯾﺞ ﺣﺎﺻﻞ از ﭘﮋوﻫﺶ ﻧﺸﺎن ﻣﯽ دﻫﺪ ﮐﻪ روش ﻣﺘﺪاول در ﻣﺤﺎﺳﺒﻪ ﻧﻮﺳﺎﻧﺎت روﻧﺪزداﯾﯽ ﺷﺪه، ﻗﺎﺑﻠﯿﺖ ﺑﺮآورد ﺣﺎﻓﻈﻪ ﺑﻠﻨﺪﻣﺪت ﻧﺮخ ارز را ﻧﺪارد، در ﺣﺎﻟﯽ ﮐﻪ ﻧﺘﺎﯾﺞ آن ﺑﺮاي ﺷﺎﺧﺺ ﺑﻮرس ﻧﺸﺎن از وﺟﻮد ﺣﺎﻓﻈﻪ ﮐﻮﺗﺎه ﻣﺪت داﺷﺖ. ﻧﺘﺎﯾﺞ ﻧﺸﺎن ﻣﯽ دﻫﺪ ﮐﻪ روش ﭘﯿﺸﻨﻬﺎدي در روﻧﺪزداﯾﯽ داده ﻫﺎ و ﻣﺤﺎﺳﺒﻪ ﻧﻮﺳﺎﻧﺎت روﻧﺪزداﯾﯽ ﺷﺪه ﻣﺒﺘﻨﯽ ﺑﺮ ﻣﺪل ﮔﺎرچ، از ﺗﻮان ﺑﺎﻻﺗﺮي در ﮐﻨﺘﺮل ﺗﻐﯿﯿﺮات ﻧﻮﺳﺎﻧﺎت ﺑﺎزار دارد و ﻃﺒﻖ ﯾﺎﻓﺘﻪ ﻫﺎي اﯾﻦ روش، ﺷﺎﺧﺺ ﺑﻮرس و ﻧﺮخ دﻻر داراي ﺣﺎﻓﻈﻪ ﺑﻠﻨﺪﻣﺪت ﺑﻮده اﻧﺪ. ﻫﻤﭽﻨﯿﻦ ﻧﺘﺎﯾﺞ ﻧﺸﺎن ﻣﯽ دﻫﺪ ﮐﻪ اﯾﻦ دو روش ﺑﺮآوردﻫﺎي ﺑﻪ ﻃﻮر ﻣﻌﻨﺎدار ﻣﺘﻔﺎوﺗﯽ از ﺣﺎﻓﻈﻪ ﺑﻠﻨﺪﻣﺪت ﺑﺎزار اراﺋﻪ ﻣﯽ دﻫﻨﺪ و ﻃﺒﻖ ﻧﺘﺎﯾﺞ آزﻣﻮن ﻫﻤﺒﺴﺘﮕﯽ ﺑﯿﻦ ﻣﻘﺎدﯾﺮ ﺣﺎﻓﻈﻪ ﺑﻠﻨﺪﻣﺪت داده ﻫﺎ و ﻣﻘﺪار ﭘﺎراﻣﺘﺮ q در ﺗﺤﻠﯿﻞ ﻧﻮﺳﺎﻧﺎت روﻧﺪزداﯾﯽ ﺷﺪه، ﻣﺸﺎﻫﺪه ﺷﺪ ﮐﻪ ﺷﺎﺧﺺ ﺑﻮرس و ﻧﺮخ ارز در اﯾﺮان داراي ﺧﺎﺻﯿﺖ ﭼﻨﺪﺑﺨﺸﯽ ﻫﺴﺘﻨﺪ.

In this study, the long-term memory of the stock market index and exchange rate (dollar) was estimated using detrended fluctuation analysis. In order to detrend the data, the GARCH approach was proposed and the long-term memory estimation model was implemented separately for both conventional and GARCH methods. For this purpose, daily data of stock market index and dollar exchange rate in the market during the years 2014 to 2020 were used. The results showed that the conventional method in calculating the detrended fluctuations is not able to estimate the long-term memory of the exchange rate, while the results for the stock index showed the existence of short-term memory. The results showed that the proposed method in detrending data and calculating detrended fluctuations based on Garch model has a higher power in controlling changes in market fluctuations and according to the findings of this method, stock index and dollar exchange rate have long-term memory. The results showed that these two methods provide significantly different estimates of long-term memory of the market and according to the results of the correlation test between the values ​​of long-term memory of data and the value of parameter q in detrended fluctuation analysis; it was observed that the stock market index and exchange rate in Iran have multifractal properties.