KRİPTO VARLIKLARDA UZUN HAFIZA VE VOLATİLİTE DİNAMİKLERİ: BITCOIN, ETHEREUM VE BINANCE COIN ÖRNEĞİ

Öz

Bu çalışmada, kripto para piyasasında en yüksek işlem hacmine sahip varlıklar arasında yer alan Bitcoin, Ethereum ve Binance Coin’in günlük kapanış fiyatları incelenmiştir. Çalışmada ele alınan kripto para getirilerinin uzun hafıza özelliği gösterip göstermediğinin belirlenmesi ve uygun model tahmininin yapılması amaçlanmıştır. Getiri serilerinin uzun hafıza özelliğinin tespit edilmesi için literatürde sıklıkla ele alınan Hurst katsayısı, Geweke ve Porter-Hudak testi ve Yerel Whittle Tahmincisi kullanılmıştır. Ayrıca uzun hafızanın tespitine yönelik klasik testlerin yanı sıra, çok değişkenli yerel Whittle Skor tipi test ve Qu (2011) tarafından önerilen uzun hafıza testleri de yapılmıştır. Elde edilen bulgulara göre üç kripto para biriminin de uzun hafıza özelliği gösterdiği tespit edilmiştir. Ardından uzun hafızanın varlığı dikkate alınarak getiri ve koşullu varyansın modellenmesi için Otoregresif Kesirli Bütünleşik Hareketli Ortalama (ARFIMA) ve Kesirli Bütünleşik Genelleştirilmiş Otoregresif Koşullu Değişen Varyans (FIGARCH) modelleri tahmin edilmiştir. Tahmin edilen FIGARCH modellerinde kesirli fark parametresi 0

Anahtar Kelimeler

• Kripto para
• Uzun hafıza
• ARFIMA
• FIGARCH

Etik Beyan

Bu çalışma kapsamında herhangi bir insan katılımcı, hayvan deneyi ya da biyolojik örnek kullanılmamıştır. Dolayısıyla etik kurul onayı gerekmemektedir.

LONG MEMORY AND VOLATILITY DYNAMICS IN CRYPTO ASSETS: THE CASES OF BITCOIN, ETHEREUM, AND BINANCE COIN

Öz

In this research, the daily closing prices of Bitcoin, Ethereum, and Binance Coin-three of the most actively traded cryptocurrencies-are analyzed. The primary objective is to investigate whether these cryptocurrencies' returns exhibit long-memory characteristics and to apply suitable model estimations. To detect the presence of long memory in the return series, well-established techniques from the literature, such as the Hurst exponent, the Geweke and Porter-Hudak test, and the Local Whittle Estimator are utilized. Additionally, advanced methodologies, including the Multivariate Local Whittle Score-type test and the long-memory test formulated by Qu (2011), are implemented. The results confirm that all three cryptocurrencies exhibit persistent memory behavior. Given this evidence, ARFIMA and FIGARCH models are employed to examine both return dynamics and conditional volatility. The FIGARCH model estimations reveal that the fractional differencing coefficient falls between 0 and 1, maintaining statistical significance across all tested cases. These findings indicate that cryptocurrency markets demonstrate long-memory traits, implying that price shocks tend to have lasting effects. The presence of long memory in these markets further suggests that historical price patterns may serve as indicators for forecasting future price movements.

Anahtar Kelimeler

• Cryptocurrency
• Long memory
• ARFIMA
• FIGARCH

Kaynakça

1. Akkuş, H. T., & Çelik, İ. (2020). Modeling, forecasting the cryptocurrency market volatility and value at risk dynamics of bitcoin. Muhasebe Bilim Dünyası Dergisi, 22(2), 296-312.
2. Al-Yahyaee, K. H., Mensi, W., Ko, H. U., Yoon, S. M., & Kang, S. H. (2020). Why cryptocurrency markets are inefficient: The impact of liquidity and volatility. The North American Journal of Economics and Finance, 52, 101168.
3. Assaf, A., Bhandari, A., Charif, H., & Demir, E. (2022). Multivariate long memory structure in the cryptocurrency market: The impact of COVID-19. International Review of Financial Analysis, 82, 102132.
4. Assaf, A., Mokni, K., Yousaf, I., & Bhandari, A. (2023). Long memory in the high frequency cryptocurrency markets using fractal connectivity analysis: The impact of COVID-19. Research in International Business and Finance, 64, 101821.
5. Baillie, R. T., Bollerslev, T., & Mikkelsen, H. O. (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of econometrics, 74(1), 3-30.
6. Betken, A. (2016). Testing for change‐points in long‐range dependent time series by means of a self‐normalized Wilcoxon test. Journal of Time Series Analysis, 37(6), 785-809.
7. Bouoiyour, J., Selmi, R., Tiwari, A. K., & Olayeni, O. R. (2016). What drives Bitcoin price. Economics Bulletin, 36(2), 843-850.
8. Briere, M., Oosterlinck, K., & Szafarz, A. (2015). Virtual currency, tangible return: Portfolio diversification with bitcoin. Journal of Asset Management, 16, 365-373.

9. Burton, G. M., & Shah, S. N. (1987). Efficient Market Hypothesis. The New Palgrave: A Dictionary of Economics, 2, 120-23.
10. Catania, L., & Grassi, S. (2022). Forecasting cryptocurrency volatility. International Journal of Forecasting, 38(3), 878-894.
11. Chkili, W. (2021). Modeling Bitcoin price volatility: Long memory vs Markov switching. Eurasian Economic Review, 11(3), 433-448.
12. Dehling, H., Rooch, A., & Taqqu, M. S. (2013). Non‐parametric change‐point tests for long‐range dependent data. Scandinavian Journal of Statistics, 40(1), 153-173.
13. Demirci, E., & Karaatlı, M. (2023). Kripto Para Fiyatlarinin LSTM Ve GRU Modelleri ile Tahmini. Journal of Mehmet Akif Ersoy University Economics and Administrative Sciences Faculty, 10(1), 134-157.
14. Duan, K., Li, Z., Urquhart, A., & Ye, J. (2021). Dynamic efficiency and arbitrage potential in Bitcoin: A long-memory approach. International Review of Financial Analysis, 75, 101725.
15. Dyhrberg, A. H. (2016). Bitcoin, gold and the dollar – A GARCH volatility analysis. Finance Research Letters, 16, 85–92.
16. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the econometric society, 987-1007.
17. Fakhfekh, M., & Jeribi, A. (2020). Volatility dynamics of crypto-currencies’ returns: Evidence from asymmetric and long memory GARCH models. Research in International Business and Finance, 51, 101075.
18. Fama, E. F. (1965). The behavior of stock-market prices. Journal of Business, 38(1), 34–105.
19. Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383–417.
20. Fama, E. F. and Blume, M. E. (1966). Filter rules and stock-market trading. The Journal of Business 39(S1), 226–241.
21. Fleischer, J. P., von Laszewski, G., Theran, C., & Parra Bautista, Y. J. (2022). Time series analysis of cryptocurrency prices using long short-term memory. Algorithms, 15(7), 230.
22. García-Enríquez, J., & Hualde, J. (2019). Local Whittle estimation of long memory: Standard versus bias-reducing techniques. Econometrics and Statistics, 12, 66-77.
23. García-Medina, A., & Aguayo-Moreno, E. (2024). LSTM–GARCH hybrid model for the prediction of volatility in cryptocurrency portfolios. Computational Economics, 63(4), 1511-1542.
24. Geweke, J., & Porter‐Hudak, S. (1983). The estimation and application of long memory time series models. Journal of time series analysis, 4(4), 221-238.
25. Gubadlı, M., & Sarıkovanlık, V. (2023). Kripto Para Piyasasinda Volatil Davranışların Asimetrik Stokastik Volatilite Modeli ile Testi. Uluslararası Yönetim İktisat ve İşletme Dergisi, 19(1), 61-82.
26. Güleç, T. C., & Aktaş, H. (2019). Kripto para birimi piyasalarında etkinliğin uzun hafıza ve değişen varyans özelliklerinin testi yoluyla analizi. Eskişehir Osmangazi Üniversitesi İktisadi ve İdari Bilimler Dergisi, 14(2), 491-510.
27. Hameed, Z., Shafi, K., & Nawab, S. (2021). Long Term Memory Effect in Selected Cryptocurrencies. Research Journal of Social Sciences and Economics Review, 2(2), 255-263.
28. Hosking, J. R. M. (1981). Fractional differencing. Biometrika, 68 (1), 165–176.
29. Iacone, F., Leybourne, S. J., & Robert Taylor, A. M. (2014). A fixed‐b test for a break in level at an unknown time under fractional integration. Journal of Time Series Analysis, 35(1), 40-54.
30. Kaya Soylu, P., Okur, M., Çatıkkaş, Ö., & Altintig, Z. A. (2020). Long memory in the volatility of selected cryptocurrencies: Bitcoin, Ethereum and Ripple. Journal of Risk and Financial Management, 13(6), 107.
31. Khan, F. U., Khan, F., & Shaikh, P. A. (2023). Forecasting returns volatility of cryptocurrency by applying various deep learning algorithms. Future Business Journal, 9(1), 25.
32. Kim, J. M., Jun, C., & Lee, J. (2021). Forecasting the volatility of the cryptocurrency market by GARCH and Stochastic Volatility. Mathematics, 9(14), 1614.
33. Kuensch, H. R. (1987, December). Statistical aspects of self-similar processes. In Proceedings of the first World Congress of the Bernoulli Society (Vol. 1, pp. 67-74). Utrecht: VNU Science Press).
34. Lahmiri, S., & Bekiros, S. (2021). The effect of COVID-19 on long memory in returns and volatility of cryptocurrency and stock markets. Chaos, Solitons & Fractals, 151, 111221.
35. Lim, K. P., & Brooks, R. (2011). The evolution of stock market efficiency over time: A survey of the empirical literature. Journal of economic surveys, 25(1), 69-108.
36. Mandelbrot, B. (1966). Forecasts of future prices, unbiased markets, and “martingale” Models. Journal of Business, 39(S1), 242–255.
37. Mensi, W., Al-Yahyaee, K. H., & Kang, S. H. (2019). Structural breaks and double long memory of cryptocurrency prices: A comparative analysis from Bitcoin and Ethereum. Finance Research Letters, 29, 222-230.
38. Münyas, T., & Aydın, G. K. (2023). Etkin piyasa hipotezi ve kripto para piyasaları üzerine bir uygulama. Alanya Akademik Bakış, 7(3), 1203-1216.
39. Nakamoto, S., & Bitcoin, A. (2008). A peer-to-peer electronic cash system. Bitcoin.–URL: https://bitcoin. org/bitcoin. pdf, 4(2), 15.
40. Nur, I. M., Nugrahanto, R., & Fauzi, F. (2023). Cryptocurrency Price Prediction: A Hybrid Long Short-Term Memory Model With Generalized Autoregressive Conditional Heteroscedasticity. BAREKENG: Journal of Mathematics and Its Applications, 17(3), 1575-1584.
41. Qu, Z. (2011). A test against spurious long memory. Journal of Business & Economic Statistics, 29(3), 423-438.
42. Rambaccussing, D., & Mazibas, M. (2020). True versus spurious long memory in cryptocurrencies. Journal of Risk and Financial Management, 13(9), 186.
43. Roberts, H. (1967). Statistical versus clinical prediction of the stock market", unpublished manuscript. Chicago, University of Chicago, Centre for Research on Security Prices.
44. Robinson, P. M. (1994). Rates of convergence and optimal spectral bandwidth for long range dependence. Probability Theory and Related Fields, 99, 443-473.
45. Robinson, P. M. (1995). Gaussian semiparametric estimation of long range dependence. The Annals of statistics, 1630-1661.
46. Samuelson, P. A. (1965). Proof that properly anticipated prices fluctuate randomly. Industrial Management Review, 6(2), 41–49.
47. Sibbertsen, P., Leschinski, C., & Busch, M. (2018). A multivariate test against spurious long memory. Journal of Econometrics, 203(1), 33-49.
48. Velasco, C. (2006). Semiparametric estimation of long-memory models. Handbook of Econometrics, 1, 353-395.
49. Wang, Y., Andreeva, G., & Martin-Barragan, B. (2023). Machine learning approaches to forecasting cryptocurrency volatility: Considering internal and external determinants. International Review of Financial Analysis, 90, 102914.
50. Wenger, K., Leschinski, C., & Sibbertsen, P. (2018). A simple test on structural change in long-memory time series. Economics Letters, 163, 90-94.
51. Wu, X., Wu, L., & Chen, S. (2022). Long memory and efficiency of Bitcoin during COVID-19. Applied Economics, 54(4), 375-389.
52. Yurttagüler, İ. (2024). Kripto Para Birimi Piyasalarında GPH Yöntemi ile Uzun Hafıza Analizi: Bitcoin Örneği. Ekonomi Politika ve Finans Araştırmaları Dergisi, 9(1), 123-139.

Ayrıntılar

Birincil Dil

Türkçe

Konular

Ekonometrik ve İstatistiksel Yöntemler, Uygulamalı Makro Ekonometri, Zaman Serileri Analizi

Bölüm

Araştırma Makalesi

Yazarlar

Nimet Melis Esenyel İçen ^*
0000-0003-1150-2535
Türkiye

Yayımlanma Tarihi

30 Haziran 2025

Gönderilme Tarihi

28 Şubat 2025

Kabul Tarihi

28 Mayıs 2025

Yayımlandığı Sayı

Yıl 2025 Cilt: 13 Sayı: 1

DOI

https://doi.org/10.52122/nisantasisbd.1648751

IZ

https://izlik.org/JA57PW82AT

Kaynak Göster

RIS / Bibtex

APA

Esenyel İçen, N. M. (2025). KRİPTO VARLIKLARDA UZUN HAFIZA VE VOLATİLİTE DİNAMİKLERİ: BITCOIN, ETHEREUM VE BINANCE COIN ÖRNEĞİ. Nişantaşı Üniversitesi Sosyal Bilimler Dergisi, 13(1), 253-269. https://doi.org/10.52122/nisantasisbd.1648751

AMA

1.Esenyel İçen NM. KRİPTO VARLIKLARDA UZUN HAFIZA VE VOLATİLİTE DİNAMİKLERİ: BITCOIN, ETHEREUM VE BINANCE COIN ÖRNEĞİ. Nişantaşı Üniversitesi Sosyal Bilimler Dergisi. 2025;13(1):253-269. doi:10.52122/nisantasisbd.1648751

Chicago

Esenyel İçen, Nimet Melis. 2025. “KRİPTO VARLIKLARDA UZUN HAFIZA VE VOLATİLİTE DİNAMİKLERİ: BITCOIN, ETHEREUM VE BINANCE COIN ÖRNEĞİ”. Nişantaşı Üniversitesi Sosyal Bilimler Dergisi 13 (1): 253-69. https://doi.org/10.52122/nisantasisbd.1648751.

EndNote

Esenyel İçen NM (01 Haziran 2025) KRİPTO VARLIKLARDA UZUN HAFIZA VE VOLATİLİTE DİNAMİKLERİ: BITCOIN, ETHEREUM VE BINANCE COIN ÖRNEĞİ. Nişantaşı Üniversitesi Sosyal Bilimler Dergisi 13 1 253–269.

IEEE

[1]N. M. Esenyel İçen, “KRİPTO VARLIKLARDA UZUN HAFIZA VE VOLATİLİTE DİNAMİKLERİ: BITCOIN, ETHEREUM VE BINANCE COIN ÖRNEĞİ”, Nişantaşı Üniversitesi Sosyal Bilimler Dergisi, c. 13, sy 1, ss. 253–269, Haz. 2025, doi: 10.52122/nisantasisbd.1648751.

ISNAD

Esenyel İçen, Nimet Melis. “KRİPTO VARLIKLARDA UZUN HAFIZA VE VOLATİLİTE DİNAMİKLERİ: BITCOIN, ETHEREUM VE BINANCE COIN ÖRNEĞİ”. Nişantaşı Üniversitesi Sosyal Bilimler Dergisi 13/1 (01 Haziran 2025): 253-269. https://doi.org/10.52122/nisantasisbd.1648751.

JAMA

1.Esenyel İçen NM. KRİPTO VARLIKLARDA UZUN HAFIZA VE VOLATİLİTE DİNAMİKLERİ: BITCOIN, ETHEREUM VE BINANCE COIN ÖRNEĞİ. Nişantaşı Üniversitesi Sosyal Bilimler Dergisi. 2025;13:253–269.

MLA

Esenyel İçen, Nimet Melis. “KRİPTO VARLIKLARDA UZUN HAFIZA VE VOLATİLİTE DİNAMİKLERİ: BITCOIN, ETHEREUM VE BINANCE COIN ÖRNEĞİ”. Nişantaşı Üniversitesi Sosyal Bilimler Dergisi, c. 13, sy 1, Haziran 2025, ss. 253-69, doi:10.52122/nisantasisbd.1648751.

Vancouver

1.Nimet Melis Esenyel İçen. KRİPTO VARLIKLARDA UZUN HAFIZA VE VOLATİLİTE DİNAMİKLERİ: BITCOIN, ETHEREUM VE BINANCE COIN ÖRNEĞİ. Nişantaşı Üniversitesi Sosyal Bilimler Dergisi. 01 Haziran 2025;13(1):253-69. doi:10.52122/nisantasisbd.1648751

LONG MEMORY AND VOLATILITY DYNAMICS IN CRYPTO ASSETS: THE CASES OF BITCOIN, ETHEREUM, AND BINANCE COIN

Öz

In this research, the daily closing prices of Bitcoin, Ethereum, and Binance Coin-three of the most actively traded cryptocurrencies-are analyzed. The primary objective is to investigate whether these cryptocurrencies' returns exhibit long-memory characteristics and to apply suitable model estimations. To detect the presence of long memory in the return series, well-established techniques from the literature, such as the Hurst exponent, the Geweke and Porter-Hudak test, and the Local Whittle Estimator are utilized. Additionally, advanced methodologies, including the Multivariate Local Whittle Score-type test and the long-memory test formulated by Qu (2011), are implemented. The results confirm that all three cryptocurrencies exhibit persistent memory behavior. Given this evidence, ARFIMA and FIGARCH models are employed to examine both return dynamics and conditional volatility. The FIGARCH model estimations reveal that the fractional differencing coefficient falls between 0 and 1, maintaining statistical significance across all tested cases. These findings indicate that cryptocurrency markets demonstrate long-memory traits, implying that price shocks tend to have lasting effects. The presence of long memory in these markets further suggests that historical price patterns may serve as indicators for forecasting future price movements.

Anahtar Kelimeler

• Cryptocurrency
• Long memory
• ARFIMA
• FIGARCH

Kaynakça

1. Akkuş, H. T., & Çelik, İ. (2020). Modeling, forecasting the cryptocurrency market volatility and value at risk dynamics of bitcoin. Muhasebe Bilim Dünyası Dergisi, 22(2), 296-312.
2. Al-Yahyaee, K. H., Mensi, W., Ko, H. U., Yoon, S. M., & Kang, S. H. (2020). Why cryptocurrency markets are inefficient: The impact of liquidity and volatility. The North American Journal of Economics and Finance, 52, 101168.
3. Assaf, A., Bhandari, A., Charif, H., & Demir, E. (2022). Multivariate long memory structure in the cryptocurrency market: The impact of COVID-19. International Review of Financial Analysis, 82, 102132.
4. Assaf, A., Mokni, K., Yousaf, I., & Bhandari, A. (2023). Long memory in the high frequency cryptocurrency markets using fractal connectivity analysis: The impact of COVID-19. Research in International Business and Finance, 64, 101821.
5. Baillie, R. T., Bollerslev, T., & Mikkelsen, H. O. (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of econometrics, 74(1), 3-30.
6. Betken, A. (2016). Testing for change‐points in long‐range dependent time series by means of a self‐normalized Wilcoxon test. Journal of Time Series Analysis, 37(6), 785-809.
7. Bouoiyour, J., Selmi, R., Tiwari, A. K., & Olayeni, O. R. (2016). What drives Bitcoin price. Economics Bulletin, 36(2), 843-850.
8. Briere, M., Oosterlinck, K., & Szafarz, A. (2015). Virtual currency, tangible return: Portfolio diversification with bitcoin. Journal of Asset Management, 16, 365-373.

9. Burton, G. M., & Shah, S. N. (1987). Efficient Market Hypothesis. The New Palgrave: A Dictionary of Economics, 2, 120-23.
10. Catania, L., & Grassi, S. (2022). Forecasting cryptocurrency volatility. International Journal of Forecasting, 38(3), 878-894.
11. Chkili, W. (2021). Modeling Bitcoin price volatility: Long memory vs Markov switching. Eurasian Economic Review, 11(3), 433-448.
12. Dehling, H., Rooch, A., & Taqqu, M. S. (2013). Non‐parametric change‐point tests for long‐range dependent data. Scandinavian Journal of Statistics, 40(1), 153-173.
13. Demirci, E., & Karaatlı, M. (2023). Kripto Para Fiyatlarinin LSTM Ve GRU Modelleri ile Tahmini. Journal of Mehmet Akif Ersoy University Economics and Administrative Sciences Faculty, 10(1), 134-157.
14. Duan, K., Li, Z., Urquhart, A., & Ye, J. (2021). Dynamic efficiency and arbitrage potential in Bitcoin: A long-memory approach. International Review of Financial Analysis, 75, 101725.
15. Dyhrberg, A. H. (2016). Bitcoin, gold and the dollar – A GARCH volatility analysis. Finance Research Letters, 16, 85–92.
16. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the econometric society, 987-1007.
17. Fakhfekh, M., & Jeribi, A. (2020). Volatility dynamics of crypto-currencies’ returns: Evidence from asymmetric and long memory GARCH models. Research in International Business and Finance, 51, 101075.
18. Fama, E. F. (1965). The behavior of stock-market prices. Journal of Business, 38(1), 34–105.
19. Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work. The Journal of Finance, 25(2), 383–417.
20. Fama, E. F. and Blume, M. E. (1966). Filter rules and stock-market trading. The Journal of Business 39(S1), 226–241.
21. Fleischer, J. P., von Laszewski, G., Theran, C., & Parra Bautista, Y. J. (2022). Time series analysis of cryptocurrency prices using long short-term memory. Algorithms, 15(7), 230.
22. García-Enríquez, J., & Hualde, J. (2019). Local Whittle estimation of long memory: Standard versus bias-reducing techniques. Econometrics and Statistics, 12, 66-77.
23. García-Medina, A., & Aguayo-Moreno, E. (2024). LSTM–GARCH hybrid model for the prediction of volatility in cryptocurrency portfolios. Computational Economics, 63(4), 1511-1542.
24. Geweke, J., & Porter‐Hudak, S. (1983). The estimation and application of long memory time series models. Journal of time series analysis, 4(4), 221-238.
25. Gubadlı, M., & Sarıkovanlık, V. (2023). Kripto Para Piyasasinda Volatil Davranışların Asimetrik Stokastik Volatilite Modeli ile Testi. Uluslararası Yönetim İktisat ve İşletme Dergisi, 19(1), 61-82.
26. Güleç, T. C., & Aktaş, H. (2019). Kripto para birimi piyasalarında etkinliğin uzun hafıza ve değişen varyans özelliklerinin testi yoluyla analizi. Eskişehir Osmangazi Üniversitesi İktisadi ve İdari Bilimler Dergisi, 14(2), 491-510.
27. Hameed, Z., Shafi, K., & Nawab, S. (2021). Long Term Memory Effect in Selected Cryptocurrencies. Research Journal of Social Sciences and Economics Review, 2(2), 255-263.
28. Hosking, J. R. M. (1981). Fractional differencing. Biometrika, 68 (1), 165–176.
29. Iacone, F., Leybourne, S. J., & Robert Taylor, A. M. (2014). A fixed‐b test for a break in level at an unknown time under fractional integration. Journal of Time Series Analysis, 35(1), 40-54.
30. Kaya Soylu, P., Okur, M., Çatıkkaş, Ö., & Altintig, Z. A. (2020). Long memory in the volatility of selected cryptocurrencies: Bitcoin, Ethereum and Ripple. Journal of Risk and Financial Management, 13(6), 107.
31. Khan, F. U., Khan, F., & Shaikh, P. A. (2023). Forecasting returns volatility of cryptocurrency by applying various deep learning algorithms. Future Business Journal, 9(1), 25.
32. Kim, J. M., Jun, C., & Lee, J. (2021). Forecasting the volatility of the cryptocurrency market by GARCH and Stochastic Volatility. Mathematics, 9(14), 1614.
33. Kuensch, H. R. (1987, December). Statistical aspects of self-similar processes. In Proceedings of the first World Congress of the Bernoulli Society (Vol. 1, pp. 67-74). Utrecht: VNU Science Press).
34. Lahmiri, S., & Bekiros, S. (2021). The effect of COVID-19 on long memory in returns and volatility of cryptocurrency and stock markets. Chaos, Solitons & Fractals, 151, 111221.
35. Lim, K. P., & Brooks, R. (2011). The evolution of stock market efficiency over time: A survey of the empirical literature. Journal of economic surveys, 25(1), 69-108.
36. Mandelbrot, B. (1966). Forecasts of future prices, unbiased markets, and “martingale” Models. Journal of Business, 39(S1), 242–255.
37. Mensi, W., Al-Yahyaee, K. H., & Kang, S. H. (2019). Structural breaks and double long memory of cryptocurrency prices: A comparative analysis from Bitcoin and Ethereum. Finance Research Letters, 29, 222-230.
38. Münyas, T., & Aydın, G. K. (2023). Etkin piyasa hipotezi ve kripto para piyasaları üzerine bir uygulama. Alanya Akademik Bakış, 7(3), 1203-1216.
39. Nakamoto, S., & Bitcoin, A. (2008). A peer-to-peer electronic cash system. Bitcoin.–URL: https://bitcoin. org/bitcoin. pdf, 4(2), 15.
40. Nur, I. M., Nugrahanto, R., & Fauzi, F. (2023). Cryptocurrency Price Prediction: A Hybrid Long Short-Term Memory Model With Generalized Autoregressive Conditional Heteroscedasticity. BAREKENG: Journal of Mathematics and Its Applications, 17(3), 1575-1584.
41. Qu, Z. (2011). A test against spurious long memory. Journal of Business & Economic Statistics, 29(3), 423-438.
42. Rambaccussing, D., & Mazibas, M. (2020). True versus spurious long memory in cryptocurrencies. Journal of Risk and Financial Management, 13(9), 186.
43. Roberts, H. (1967). Statistical versus clinical prediction of the stock market", unpublished manuscript. Chicago, University of Chicago, Centre for Research on Security Prices.
44. Robinson, P. M. (1994). Rates of convergence and optimal spectral bandwidth for long range dependence. Probability Theory and Related Fields, 99, 443-473.
45. Robinson, P. M. (1995). Gaussian semiparametric estimation of long range dependence. The Annals of statistics, 1630-1661.
46. Samuelson, P. A. (1965). Proof that properly anticipated prices fluctuate randomly. Industrial Management Review, 6(2), 41–49.
47. Sibbertsen, P., Leschinski, C., & Busch, M. (2018). A multivariate test against spurious long memory. Journal of Econometrics, 203(1), 33-49.
48. Velasco, C. (2006). Semiparametric estimation of long-memory models. Handbook of Econometrics, 1, 353-395.
49. Wang, Y., Andreeva, G., & Martin-Barragan, B. (2023). Machine learning approaches to forecasting cryptocurrency volatility: Considering internal and external determinants. International Review of Financial Analysis, 90, 102914.
50. Wenger, K., Leschinski, C., & Sibbertsen, P. (2018). A simple test on structural change in long-memory time series. Economics Letters, 163, 90-94.
51. Wu, X., Wu, L., & Chen, S. (2022). Long memory and efficiency of Bitcoin during COVID-19. Applied Economics, 54(4), 375-389.
52. Yurttagüler, İ. (2024). Kripto Para Birimi Piyasalarında GPH Yöntemi ile Uzun Hafıza Analizi: Bitcoin Örneği. Ekonomi Politika ve Finans Araştırmaları Dergisi, 9(1), 123-139.