INVESTIGATION OF LONG MEMORY AND STOCHASTIC PROPERTIES OF HIGH FREQUENCY CRYPTO ASSET VOLATİLİTY BY FIGARCH MODELING

Year 2022, Volume: 12 Issue: 24, 284 - 310, 28.11.2022

Volkan Eteman , Erkan Işığıçok

https://doi.org/10.53092/duiibfd.1124966

Abstract

In this study, it is aimed to comparatively examine the volatility models and long memory properties of high frequency intraday asset returns of selected crypto assets. Bitcoin (BTC), Ethereum (ETH), Cardano (ADA) and Binance Coin (BNB) 4 different crypto assets, 1-day, 12-hour, 8-hour, 6-hour, 4-hour, 2-hour, 1-hour, 30 minute and 15 minute frequency levels are the subject of the study. The 36 data sets examined are discussed in the FIGARCH (Fractional Integrated-GARCH) model. As a result of the analysis, it has been determined that all series have long memory feature, except for the ETH 30-minute return series. It was determined that the errors were not independently and randomly distributed with the increase in the sampling frequency. It was concluded that the long memory parameters of different sampling frequencies were similar to each other on average. however, there are findings that various frequencies of some assets can create an advantageous investment strategy. By providing all the conditions and constraints with the FIGARCH model, it was determined that 35 of 36 datasets were successful in modeling as meaningful and well-defined.

Keywords

Long Memory, Crytptocurrency Market, High Frequency Data, Figarch

YÜKSEK FREKANSLI KRİPTO VARLIK OYNAKLIĞININ UZUN HAFIZA VE STOKASTİK ÖZELLİKLERİNİN FIGARCH MODELİ İLE İNCELENMESİ

Abstract

Bu çalışmada, seçilmiş kripto varlıkların yüksek frekanslı gün içi varlık getirilerinin oynaklık (volatility) modelleri ve uzun hafıza özelliklerinin karşılaştırılmalı olarak incelenmesi amaçlanmıştır. Bitcoin (BTC), Ethereum (ETH), Cardano (ADA) ve Binance Coin (BNB) olmak üzere, 4 farklı kripto varlığın, 1 günlük, 12 saatlik, 8 saatlik, 6 saatlik, 4 saatlik, 2 saatlik, 1 saatlik, 30 dakikalık ve 15 dakikalık frekans düzeylerinde gerçekleşen 36 getiri serisi FIGARCH (Fractional Integrated- Kesirli Bütünleşik/Entegre edilmiş GARCH) modeli özelinde ele alınmıştır. Yapılan analizler sonucunda, ETH 30 dakikalık getiri serisi dışında, tüm serilerde uzun hafıza özelliğinin mevcut olduğu belirlenmiştir. Örneklem frekansının artması ile hataların bağımsız ve rassal dağılmakta güçlük çektiği, farklı örneklem frekanslarının uzun hafıza parametrelerinin ortalama olarak birbirine benzer olduğu, ancak bazı varlıkların çeşitli frekanslarının avantajlı bir yatırım stratejisi oluşturabileceği yönünde bulgular elde edilmiştir. FIGARCH modeli ile tüm koşul ve kısıtlar sağlanarak, 36 veri kümesinin 35’inin anlamlı ve iyi tanımlanmış olarak modellemede başarılı olduğu belirlenmiştir.

Keywords

Figarch, Uzun Hafıza, Kripto Para Piyasası, Yüksek Frekanslı Veri, Long Memory, Crytptocurrency Market, High Frequency Data

References

• Bariviera, A. F., Zunino, L., & Rosso, O. A. (2018). An analysis of high-frequency cryptocurrencies prices dynamics using permutation-information-theory quantifiers. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28. https://doi.org/https://doi.org/10.1063/1.5027153
• Akkuş, H. T., & Çelik, İ. (2020). Modelling, Forecasting the Cryptocurrency Market Volatility and Value At Risk Dynamics of Bitcoin. Muhasebe Bilim Dünyası Dergisi, 22(2), 296-312. https://doi.org/https://doi.org/10.31460/mbdd.726952
• Baillie, R. T., Bollerslev, T., & Mikkelsen, H. O. (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 74.
• Baillie, R., Han, Y. W., & Myers, R. (2007). Long Memory and FIGARCH Models for Daily and High Frequency Commodity Prices. Queen Mary, University of London, School of Economics and Finance, Working Papers.
• Balıbey, M. (2014). İkili Uzun Hafıza Modelleri: Bazı Makroekonomik Değişkenler Üzerine Bir Uygulama. BİLECİK,: BİLECİK ŞEYH EDEBALİ ÜNİVERSİTESİ.
• Bariviera,, A. F. (2017). The inefficiency of Bitcoin revisited: A dynamic approach. Economics Letters, 161, 1-4. https://doi.org/https://doi.org/10.1016/j.econlet.2017.09.013.
• Beran, J. (1994). Statistics for Long-Memory Processes. Chaman & Hall.
• Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31, 307-327.
• Catania, L., & Sandholdt, M. (2019). Bitcoin at High Frequency. J. Risk Financial Management, 12(36). https://doi.org/doi:10.3390/jrfm12010036
• coinmarketcap. (2022). https://coinmarketcap.com/tr/. 05 8, 2022 tarihinde https://coinmarketcap.com/tr/?page=102: https://coinmarketcap.com/tr/?page=102 adresinden alındı
• Çil, N. (2018). Finansal Ekonometri. İstanbul: DER Kitapevi Yayınevi.
• Dyhrberg, A. H. (2016). Bitcoin,gold and the dollar – A GARCH volatility analysis. Finance Research Letters, 16, 85-92. https://doi.org/https://doi.org/10.1016/j.frl.2015.10.008
• Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4), 987-1007.
• Fama, E. F. (1970). Efficient Capital Markets: A Review of Theory and Empirical Work. The Journal of Finance, 25(2), 383-417. https://doi.org/10.2307/2325486
• Galanos, A. (2022, 04 19). Package ‘rugarch’. Univariate GARCH Models: https://cran.r-project.org/web/packages/rugarch/rugarch.pdf adresinden alındı
• Gençyürek, A. G. (2019). Sermaye Piyasasında İkili Uzun Hafıza ve Emtia Volatiliteleri Geçişkenliği. İzmir: DOKUZ EYLÜL ÜNİVERSİTESİ SOSYAL BİLİMLER ENSTİTÜSÜ İŞLETME ANABİLİM DALI.
• Granger, C. W., & Joyeux, R. (1980). An Introduction to Long-Memory Tıme Series Models And Fractional Differencing. Journal Of Time Series Analysis, 1(1), 15-29. https://doi.org/https://doi.org/10.1111/j.1467-9892.1980.tb00297.x
• Gronwald, M. (2014). The Economics of Bitcoins - Market Characteristics and Price Jumps. CESifo Working Paper Series.
• Güleç, T. C., & Aktaş, H. (2019). Kripto Para Birimi PiyasalarındaEtkinliğin Uzun Hafıza ve Değişen Varyans Özelliklerinin Testi Yoluyla Analizi. Eskişehir Osmangazi Üniversitesi İİBF Dergisi, 4(2), 491-510.
• Gyamera, S. A. (2019). Modelling the volatility of Bitcoin returns using GARCH models. Quantitative Finance and Economics. https://doi.org/DOI:10.3934/QFE.2019.4.739
• Han, Y. W. (2019). Long Memory Volatility and Bernoulli Jumps in Daily Crypto Currency Prices. Journal of Insurance and Finance, 109-138. https://doi.org/https://doi.org/10.23842/jif.2019.30.4.004
• Hosking, J. M. (1981). Fractional Differencing. Biometrika, 68(1), 165-176.
• Irena, , B., & Nino, A. F. (2021). Time-Varying Volatility in Bitcoin Market and Information Flow at Minute-Level Frequency. Frontiers in Physics, 9. https://doi.org/10.3389/fphy.2021.644102
• Işığıçok, E. (1999). Türkiye'de Enflasyon'un Varyansının ARCH ve GARCH Modelleri İle Tahmini. Uludağ Üniversitesi İİBF Dergisi.
• Johnson, B. (2010). Algorithmic trading & DMA An İntroduction Direct Access Trading Strategies. london: Myeloma.
• Katsiampa, P., Corbet, S., & Lucey, B. (2019). High frequency volatility co-movements in cryptocurrency markets. Journal of International Financial Markets, Institutions and Money, 62, 35-52. https://doi.org/https://doi.org/10.1016/j.intfin.2019.05.003.
• Kazova, F., & Ercan Büyükyılmaz , A. (2021). Kripto Para Birimlerinin Volatilite Yapılarının Karşılaştırmalı Analizi. Journal of Econometrics and Statistics, 35-57.
• McHardy, S. (2022, 4 9). Welcome to python-binance v1.0.16. https://python-binance.readthedocs.io/en/latest/ adresinden alındı
• Mensi, W., Rehman, M. U., Shafiullah, M., Al-Yahyaee, K. H., & Şensoy, A. (2021). High frequency multiscale relationships among major cryptocurrencies: portfolio management implications. Financial Innovation. https://doi.org/https://doi.org/10.1186/s40854-021-00290-w
• Nuti, G., Mirghaemi, M., Treleaven, P., & Yingsaeree, C. (2011). Algorithmic Trading. londra: IEEE Computer Society.
• Peng, Y., Albuquerque, P. H., de Sá, J. M., Padula, A. J., & Montenegro, M. R. (2018). The best of two worlds: Forecasting high frequency volatility for cryptocurrencies and traditional currencies with Support Vector Regression. Expert Systems with Applications, 97, 177-192. https://doi.org/https://doi.org/10.1016/j.eswa.2017.12.004.
• Phillip, A., Chan, J. S., & Peiris, S. (2018). A new look at Cryptocurrencies. Economics Letters, 163, 6-9. https://doi.org/10.1016/j.econlet.2017.11.020.
• Phister, M. J. (1989). Quotron II: An Eairly Multiprogrammed Multiprocessor for the Communication of Stock Market Data. Annals of the History of Computing, 109-126.
• Riordan, R. J. (2009, 08 04). The Economics of Algorithmic Trading. Karlsruhe: Universität Karlsruhe.
• Seabold, Skipper, & Josef, P. (2010). statsmodels: Econometric and statistical modeling with python. https://www.statsmodels.org/. adresinden alındı
• Soylu Kaya, P., Okur, M., Çatıktaş, Ö., & Altintiğ, Z. A. (2020). Long Memory in the Volatility of Selected Cryptocurrencies: Bitcoin, Ethereum and Ripple. Journal of Risk and Financial Management, 13. https://doi.org/https://doi.org/10.3390/jrfm13060107
• Söylemez, Y. (2020). Genelleştirilmiş Otoregresif Koşullu Değişen Varyans Modelleri İle Bitcoin Volatilitesinin Analizi. Journal of Business Research - Turk, 12(2), 1322-1333. https://doi.org/10.20491/isarder.2020.914
• Treleaven, P., Galas, M., & lalchand, V. (2013). Algorithmic Trading Review. communications of the acm, 76-85.
• Urquhart, A. (2017). Price clustering in Bitcoin. Economics Letters, 159, 145-148. https://doi.org/https://doi.org/10.1016/j.econlet.2017.07.035.
• Wright, D. J. (1989). Technology and Performance: The Evolution of Market Mechanisms. Business Horizons, 65-69.