Communications for Statistical Applications and Methods

  • 제28권5호
  • /
  • Pages.511-520
  • /
  • 2021
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

Change point analysis in Bitcoin return series : a robust approach

  • Song, Junmo (Department of Statistics, Kyungpook National University) ;
  • Kang, Jiwon (Department of Computer Science and Statistics, Jeju National University)
  • 투고 : 2021.04.09
  • 심사 : 2021.05.21
  • 발행 : 2021.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Over the last decade, Bitcoin has attracted a great deal of public interest and Bitcoin market has grown rapidly. One of the main characteristics of the market is that it often undergoes some events or incidents that cause outlying observations. To obtain reliable results in the statistical analysis of Bitcoin data, these outlying observations need to be carefully treated. In this study, we are interested in change point analysis for Bitcoin return series having such outlying observations. Since these outlying observations can affect change point analysis undesirably, we use a robust test for parameter change to locate change points. We report some significant change points that are not detected by the existing tests and demonstrate that the model allowing for parameter changes is better fitted to the data. Finally, we show that the model with parameter change can improve the forecasting performance of Value-at-Risk.

키워드

과제정보

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1I1A3A01056924) (J. Song) and by the 2020 scientific promotion program funded by Jeju National University (J. Kang).

참고문헌

  1. Ardia D, Bluteau K, and Ruede, M (2019). Regime changes in bitcoin GARCH volatility dynamics, Finance Research Letters, 29, 266-271. https://doi.org/10.1016/j.frl.2018.08.009
  2. Aue A and Horvath L (2013). Structural breaks in time series, Journal of Time Series Analysis, 34, 1-16. https://doi.org/10.1111/j.1467-9892.2012.00819.x
  3. Bariviera AF, Basgall MJ, Hasperue W, and Naiouf M (2017). Some stylized facts of the bitcoin market, Physica A: Statistical Mechanics and its Applications, 484, 82-90. https://doi.org/10.1016/j.physa.2017.04.159
  4. Berkes I,Horvath L, and Kokoszka P (2004). Testing for parameter constancy in GARCH(p,q) models, Statistics & Probability Letters, 4, 263-273.
  5. Canh NP, Wongchoti U, Thanh SD, and Thong NT (2019). Systematic risk in cryptocurrency market: Evidence from DCC-MGARCH model, Finance Research Letters, 29, 90-100. https://doi.org/10.1016/j.frl.2019.03.011
  6. Caporale GM, Gil-Alana L, and Plastun A (2018). Persistence in the cryptocurrency market, Research in International Business and Finance, 46, 141-148. https://doi.org/10.1016/j.ribaf.2018.01.002
  7. Caporale GM and Zekokh T (2019). Modelling volatility of cryptocurrencies using Markov- Switching GARCH models, Research in International Business and Finance, 48, 143-155. https://doi.org/10.1016/j.ribaf.2018.12.009
  8. Chaim P and Laurini MP (2018). Volatility and return jumps in bitcoin, Economics Letters, 173, 158-163. https://doi.org/10.1016/j.econlet.2018.10.011
  9. Chen C and Liu LM (1993). Joint estimation of model parameters and outlier effects in time series, Journal of the American Statistical Association, 88, 284-297. https://doi.org/10.2307/2290724
  10. Chu J, Chan S, Nadarajah S, and Osterrieder J (2017). GARCH modelling of cryptocurrencies, Journal of Risk and Financial Management, 10, 17. https://doi.org/10.3390/jrfm10040017
  11. Fearnhead P and Rigaill G (2019). Change point detection in the presence of outliers, Journal of the American Statistical Association, 114, 169-183. https://doi.org/10.1080/01621459.2017.1385466
  12. Franses PH and Ghijsels H (1999). Additive outliers, GARCH and forecasting volatility, International Journal of forecasting, 15, 1-9. https://doi.org/10.1016/S0169-2070(98)00053-3
  13. Glaser F, Zimmermann K, Haferkorn M, Weber MC, and Siering M (2014). Bitcoin-asset or currency? revealing users' hidden intentions, Revealing Users' Hidden Intentions (April 15, 2014). ECIS 2014(Tel Aviv).
  14. Horvath L and Rice G (2014). Extensions of some classical methods in change point analysis, TEST, 23, 219-255. https://doi.org/10.1007/s11749-014-0368-4
  15. Hwang S and Basawa I (2004). Stationarity and moment structure for Box-Cox transformed threshold GARCH (1, 1) processes, Statistics & Probability Letters, 68, 209-220. https://doi.org/10.1016/j.spl.2003.08.016
  16. Jiang Y, Nie H, and Ruan W (2018). Time-varying long-term memory in bitcoin market, Finance Research Letter, 25, 280-284. https://doi.org/10.1016/j.frl.2017.12.009
  17. Katsiampa P (2017). Volatility estimation for bitcoin: A comparison of GARCH models, Economics Letters, 158, 3-6. https://doi.org/10.1016/j.econlet.2017.06.023
  18. Kulperger R and Yu H (2005). High moment partial sum processes of residuals in GARCH models and their applications, The Annals of Statistics, 33, 2395-2422. https://doi.org/10.1214/009053605000000534
  19. Kupiec P (1995). Techniques for verifying the accuracy of risk measurement models, The Journal of Derivatives, 3, 73-84. https://doi.org/10.3905/jod.1995.407942
  20. Lee S and Song J (2009). Minimum density power divergence estimator for GARCH models, TEST, 18, 316-341. https://doi.org/10.1007/s11749-008-0093-y
  21. Mensi W, Al-Yahyaee KH, and Kang SH (2019). Structural breaks and double long memory of cryptocurrency prices: A comparative analysis from bitcoin and ethereum, Finance Research Letters, 29, 222-230. https://doi.org/10.1016/j.frl.2018.07.011
  22. Ninomiya Y (2015). Change-point model selection via AIC, Annals of the Institute of Statistical Mathematics, 67, 943-961. https://doi.org/10.1007/s10463-014-0481-x
  23. Pan J, Wang H, and Tong H (2008). Estimation and tests for power-transformed and threshold GARCH models, Journal of Econometrics, 142, 352-378. https://doi.org/10.1016/j.jeconom.2007.06.004
  24. Song J and Kang J (2018). Parameter change tests for ARMA-GARCH models, Computational Statistics & Data Analysis, 121, 41-56. https://doi.org/10.1016/j.csda.2017.12.002
  25. Song J and Kang J (2021). Test for parameter change in the presence of outliers: the density power divergence based approach, Journal of Statistical Computation and Simulation, 5, 1016-1039. https://doi.org/10.1080/00949655.2020.1842407
  26. Thies S and Molnar P (2018). Bayesian change point analysis of bitcoin returns, Finance Research Letters, 27, 223-227. https://doi.org/10.1016/j.frl.2018.03.018
  27. Tiwari AK, Kumar S, and Pathak R (2019). Modelling the dynamics of bitcoin and litecoin: GARCH versus stochastic volatility models, Applied Economics, 51, 4073-4082. https://doi.org/10.1080/00036846.2019.1588951
  28. Tsay RS (1988). Outliers, level shifts, and variance changes in time series, Journal of forecasting, 7, 1-20. https://doi.org/10.1002/for.3980070102