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Noncausal Autoregressive Model in Application to Bitcoin/USD Exchange Rates

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Econometrics of Risk

Part of the book series: Studies in Computational Intelligence ((SCI,volume 583))

Abstract

This paper introduces a noncausal autoregressive process with Cauchy errors in application to the exchange rates of the Bitcoin electronic currency against the US Dollar. The dynamics of the daily Bitcoin/USD exchange rate series displays episodes of local trends, which can be modelled and interpreted as speculative bubbles. The bubbles may result from the speculative component in the on-line trading. The Bitcoin/USD exchange rates are modelled and predicted.

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Notes

  1. 1.

    Formerly magic: the gathering online exchange.

  2. 2.

    The transactions on this market have been suspended as of February 25, 2014. The reason is yet to be revealed, but an attack by hackers has been declared.

  3. 3.

    It represented 12  % of the trades before it collapsed.

  4. 4.

    The difference between the sample max and min.

  5. 5.

    See e.g. [13], [33, Theorem 1.3.1.], for errors with finite variance, Breidt [10] for errors with finite expectation and infinite variance, [22] for errors without finite expectation, as the Cauchy errors considered in the application.

  6. 6.

    The approximate likelihood disregards the first \(r\) state variables that summarize the effect of shocks before time \(r\) and the last \(s\) state variables that summarize the effect of shocks after time \(T-s\) [21, 22] and is therefore constructed from shocks \(e_{r+1}, \dots e_{T-s-1}\) only.

  7. 7.

    Alternatively, it can be represented by a model with a stochastic trend, assumed independent of the shocks that create the speculative bubble.

  8. 8.

    The French platform Bitcoin-Central has been closed for 5 months in 2013 due to hackers attack. Nevertheless the customers had still the possibility to withdraw their bitcoins.

References

  1. Andrews, B., Calder, M., Davis, R.: Maximum likelihood estimation for \(\alpha \)-stable autoregressive processes. Ann. Stat. 37, 1946–1982 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Andrews, B., Davis, R.: Model identification for infinite variance autoregressive processes. J. Econom. 172, 222–234 (2013)

    Article  MathSciNet  Google Scholar 

  3. Balkema, G., Embrechts, P., Nolde, N.: The shape of asymptotic dependence. In: Shirayev, A., Varadhan, S., Presman, E. (eds.) Springer Proceedings in Mathematics and Statistics, special volume. Prokhorov and Contemporary Probability Theory, vol. 33, pp. 43–67 (2013)

    Google Scholar 

  4. Blanchard, O.: Speculative bubbles: crashes and rational expectations. Econ. Lett. 3, 387–389 (1979)

    Article  Google Scholar 

  5. Blanchard, O., Watson, M.: Bubbles, rational expectations and financial markets. In: Wachtel, P. (ed.) Crisis in the Economic and Financial Structure, pp. 295–315, Lexington (1982)

    Google Scholar 

  6. Bitcoin: Introduction. Retrieved 4 December 2013, https://en.bitcoin.it/wiki/Introduction (2013)

  7. Bitcoin: Controlled Supply. Retrieved 4 December 2013, https://en.bitcoin.it/wiki/Controlled_Currency_Supply (2013)

  8. Bitcoin: Trade. Retrieved 4 December 2013, https://en.bitcoin.it/wiki/Trade (2013)

  9. Blockchain. Bitcoin Market Capitalization. Retrieved from Bitcoin Block Explorer, http://blockchain.info/charts/market_cap

  10. Breidt, F., Davis, R.: Time reversibility, identifiability and independence of innovations for stationary time series. J. Time Ser. Anal. 13, 273–390 (1992)

    Article  MathSciNet  Google Scholar 

  11. Breidt, F., Davis, R., Lii, K.: Maximum likelihood estimation for noncausal autoregressive processes. J. Multivar. Anal. 36, 175–198 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  12. Brunnermeier, M.: Asset Pricing under Asymmetric Information: Bubbles, Crashes, Technical Analysis and Herding. Oxford University Press, Oxford (2001)

    Book  Google Scholar 

  13. Cheng, Q.: On the unique representation of non-Gaussian linear processes. Ann. Stat. 20, 1143–1145 (1992)

    Article  MATH  Google Scholar 

  14. Davis, J.: The Crypto-Currency, The New Yorker. Retrieved from http://www.newyorker.com/reporting/2011/10/10/111010fa_fact_davis (2011)

  15. Davis, R., Resnick, S.: Limit theory for moving averages of random variables with regularly varying tail probabilities. Ann. Probab. 13, 179–195 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  16. Davis, R., Resnick, S.: Limit theory for the sample covariance and correlation functions of moving averages. Ann. Stat. 14, 533–558 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  17. Davis, R., Song, L.: Noncausal Vector AR Processes with Application to Economic Time Series, DP Columbia University (2012)

    Google Scholar 

  18. Evans, G.: Pitfalls in testing for explosive bubbles in asset prices. Am. Econ. Rev. 81, 922–930 (1991)

    Google Scholar 

  19. Flitter, E.: FBI shuts alleged online drug marketplace, Silk Road, Reuters. Retrieved from http://www.reuters.com/article/2013/10/02/us-crime-silkroad-raid-idUSBRE9910TR20131002 (2013)

  20. Gourieroux, C., Jasiak, J.: Filtering, Prediction and Estimation of Noncausal Processes. CREST (2014)

    Google Scholar 

  21. Gourieroux, C., Zakoian, J.M.: Explosive Bubble Modelling by Noncausal Cauchy Autoregressive Process. CREST (2013)

    Google Scholar 

  22. Gourieroux, C., Zakoian, J.M.: On Uniqueness of Moving Average Representation of Heavy Tailed Stationary Processes. CREST (2013)

    Google Scholar 

  23. Lanne, M., Saikkonen, P.: Noncausal autoregressions for economic time series. J. Time Ser. Econom. 3(3), Article 2 (2011)

    Google Scholar 

  24. Lanne, M., Luoto, J., Saikkonen, P.: Optimal forecasting of nonlinear autoregressive time series. Int. J. Forecast. 28, 623–631 (2010)

    Article  Google Scholar 

  25. Lanne, M., Saikkonen, P.: Noncausal vector autoregression. Econom. Theory 29, 447–481 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  26. Li, S.: Bitcoin now accepted as tuition payment at a Cyprus University, Los Angeles Times. Retrieved from http://www.latimes.com/business/money/la-fi-mo-cyprus-university-bitcoin-20131120,0,3194094.story#axzz2mXKIff7E (2013)

  27. Litecoin Block Explorer: Litecoin Block Explorer Charts. Retrieved from 4 December 2013, http://ltc.block-explorer.com/charts (2013)

  28. Liu, J.: BTC China the world’s largest Bitcoin trading platform, ZD Net. Retrieved from http://www.zdnet.com/btc-china-the-worlds-largest-bitcoin-trading-platform-7000023316/ (2013)

  29. Muth, J.: Rational expectations and the theory of price movements. Econometrica 29, 315–335 (1961)

    Article  Google Scholar 

  30. Newbold, P.: The exact likelihood function for a mixed autoregressive-moving average process. Biometrika. 61, 423– 426 (1974)

    Google Scholar 

  31. Phillips, P., Shi, S., Yu, J.: Testing for Multiple Bubbles, DP Cowles Foundation, 1843 (2012)

    Google Scholar 

  32. Phillips, P., Wu, Y., Yu, J.: Explosive behavior in the 1990s Nasdaq: when did exuberance escalate asset values? Int. Econ. Rev. 52, 201–226 (2011)

    Article  Google Scholar 

  33. Rosenblatt, M.: Gaussian and Non-Gaussian Linear Time Series and Random Fields. Springer, New York (2000)

    Book  MATH  Google Scholar 

  34. Sparshott, J.: Web Money Gets Laundering Rule, The Wall Street Journal. Retrieved  from http://online.wsj.com/news/articles/SB10001424127887324373204578374611351125202  (2013)

  35. Tagaris, K.: Cyprus details heavy losses for major bank customers, Reuters. Retrieved from http://www.reuters.com/article/2013/03/30/us-cyprus-parliament-idUSBRE92G03I20130330 (2013)

  36. Velde, F.R.: Bitcoin: A primer, Chicago Fed Letter. Retrieved from http://www.chicagofed.org/digital_assets/publications/chicago_fed_letter/2013/cfldecember2013_317.pdf (2013)

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Authors and Affiliations

  1. York University, Department of Economics, 4700 Keele St, Toronto, ON, M3J 1P3, Canada

    Andrew Hencic

  2. University of Toronto and CREST, Max Gluskin House, 150 St. George Street, Toronto, ON, M5S 3G7, Canada

    Christian Gouriéroux

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  1. Andrew Hencic
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  2. Christian Gouriéroux
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Correspondence to Christian Gouriéroux .

Editor information

Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Nomi, Japan

    Van-Nam Huynh

  2. Department of Computer Science, University of Texas at El Paso, El Paso, Texas, USA

    Vladik Kreinovich

  3. Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand

    Songsak Sriboonchitta

  4. Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand

    Komsan Suriya

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Hencic, A., Gouriéroux, C. (2015). Noncausal Autoregressive Model in Application to Bitcoin/USD Exchange Rates. In: Huynh, VN., Kreinovich, V., Sriboonchitta, S., Suriya, K. (eds) Econometrics of Risk. Studies in Computational Intelligence, vol 583. Springer, Cham. https://doi.org/10.1007/978-3-319-13449-9_2

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  • DOI: https://doi.org/10.1007/978-3-319-13449-9_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13448-2

  • Online ISBN: 978-3-319-13449-9

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