Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/hhs/cbsnow/2020_020.html
   My bibliography  Save this paper

Forecasting Mid-price Movement of Bitcoin Futures Using Machine Learning

Author

Listed:
  • Akyildirim, Erdinc

    (Department of Mathematics, ETH, Zurich, Switzerland and University of Zurich, Department of Banking and Finance, Zurich, Switzerland and Department of Banking and Finance, Burdur Mehmet Akif Ersoy University, Burdur, Turkey)

  • Cepni, Oguzhan

    (Department of Economics, Copenhagen Business School)

  • Corbet, Shaen

    (DCU Business School, Dublin City University, Dublin 9, Ireland and School of Accounting, Finance and Economics, University of Waikato, New Zealand)

  • Uddin, Gazi Salah

    (Department of Management and Engineering, Linköping University, 581 83 Linköping, Sweden)

Abstract
In the aftermath of the global financial crisis and on-going COVID-19, investors face challenges in understanding price dynamics across assets. In this paper, we explore the applicability of a large scale comparison of machine learning algorithms (MLA) to predict mid-price movement for bitcoin futures prices. We use high-frequency intra-day data to evaluate the relative forecasting performances across various time-frequencies, ranging between 5-minutes and 60-minutes. The empirical analysis is based on six different specifications of MLA methods during periods of pandemic. The empirical results show that MLA outperforms the random walk and ARIMA forecasts in Bitcoin futures markets, which may have important implications in the decision-making process of predictability.

Suggested Citation

  • Akyildirim, Erdinc & Cepni, Oguzhan & Corbet, Shaen & Uddin, Gazi Salah, 2020. "Forecasting Mid-price Movement of Bitcoin Futures Using Machine Learning," Working Papers 20-2020, Copenhagen Business School, Department of Economics.
    • Handle: RePEc:hhs:cbsnow:2020_020
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10398/1f7d2c7c-110a-4972-a4c4-47da5119ebd8
    File Function: Full text
    Download Restriction: Full text not avaiable
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dimitrios Koutmos, 2020. "Market risk and Bitcoin returns," Annals of Operations Research, Springer, vol. 294(1), pages 453-477, November.
    2. Atsalakis, George S. & Atsalaki, Ioanna G. & Pasiouras, Fotios & Zopounidis, Constantin, 2019. "Bitcoin price forecasting with neuro-fuzzy techniques," European Journal of Operational Research, Elsevier, vol. 276(2), pages 770-780.
    3. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2018. "Bitcoin technical trading with artificial neural network," CIRJE F-Series CIRJE-F-1078, CIRJE, Faculty of Economics, University of Tokyo.
    4. Vasilios Plakandaras & Theophilos Papadimitriou & Periklis Gogas, 2015. "Forecasting Daily and Monthly Exchange Rates with Machine Learning Techniques," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(7), pages 560-573, November.
    5. Kim, A. & Yang, Y. & Lessmann, S. & Ma, T. & Sung, M.-C. & Johnson, J.E.V., 2020. "Can deep learning predict risky retail investors? A case study in financial risk behavior forecasting," European Journal of Operational Research, Elsevier, vol. 283(1), pages 217-234.
    6. Sánchez Lasheras, Fernando & de Cos Juez, Francisco Javier & Suárez Sánchez, Ana & Krzemień, Alicja & Riesgo Fernández, Pedro, 2015. "Forecasting the COMEX copper spot price by means of neural networks and ARIMA models," Resources Policy, Elsevier, vol. 45(C), pages 37-43.
    7. Yongmei Fang & Bo Guan & Shangjuan Wu & Saeed Heravi, 2020. "Optimal forecast combination based on ensemble empirical mode decomposition for agricultural commodity futures prices," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(6), pages 877-886, September.
    8. Sensoy, Ahmet, 2019. "The inefficiency of Bitcoin revisited: A high-frequency analysis with alternative currencies," Finance Research Letters, Elsevier, vol. 28(C), pages 68-73.
    9. Shaen Corbet & Charles Larkin & Brian M. Lucey & Andrew Meegan & Larisa Yarovaya, 2020. "The impact of macroeconomic news on Bitcoin returns," The European Journal of Finance, Taylor & Francis Journals, vol. 26(14), pages 1396-1416, September.
    10. Chowdhury, Reaz & Rahman, M. Arifur & Rahman, M. Sohel & Mahdy, M.R.C., 2020. "An approach to predict and forecast the price of constituents and index of cryptocurrency using machine learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    11. Akyildirim, Erdinç & Corbet, Shaen & Cumming, Douglas & Lucey, Brian & Sensoy, Ahmet, 2020. "Riding the Wave of Crypto-Exuberance: The Potential Misusage of Corporate Blockchain Announcements," Technological Forecasting and Social Change, Elsevier, vol. 159(C).
    12. Yinghao Chen & Xiaoliang Xie & Tianle Zhang & Jiaxian Bai & Muzhou Hou, 2020. "A deep residual compensation extreme learning machine and applications," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(6), pages 986-999, September.
    13. Wittkemper, Hans-Georg & Steiner, Manfred, 1996. "Using neural networks to forecast the systematic risk of stocks," European Journal of Operational Research, Elsevier, vol. 90(3), pages 577-588, May.
    14. El Shazly, Mona R. & El Shazly, Hassan E., 1999. "Forecasting currency prices using a genetically evolved neural network architecture," International Review of Financial Analysis, Elsevier, vol. 8(1), pages 67-82.
    15. Alameer, Zakaria & Fathalla, Ahmed & Li, Kenli & Ye, Haiwang & Jianhua, Zhang, 2020. "Multistep-ahead forecasting of coal prices using a hybrid deep learning model," Resources Policy, Elsevier, vol. 65(C).
    16. Akhtaruzzaman, Md & Boubaker, Sabri & Sensoy, Ahmet, 2021. "Financial contagion during COVID–19 crisis," Finance Research Letters, Elsevier, vol. 38(C).
    17. Justin A. Sirignano, 2019. "Deep learning for limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 19(4), pages 549-570, April.
    18. Matyjaszek, Marta & Riesgo Fernández, Pedro & Krzemień, Alicja & Wodarski, Krzysztof & Fidalgo Valverde, Gregorio, 2019. "Forecasting coking coal prices by means of ARIMA models and neural networks, considering the transgenic time series theory," Resources Policy, Elsevier, vol. 61(C), pages 283-292.
    19. Chai, Jian & Xing, Li-Min & Zhou, Xiao-Yang & Zhang, Zhe George & Li, Jie-Xun, 2018. "Forecasting the WTI crude oil price by a hybrid-refined method," Energy Economics, Elsevier, vol. 71(C), pages 114-127.
    20. Auld, Tom & Linton, Oliver, 2019. "The behaviour of betting and currency markets on the night of the EU referendum," International Journal of Forecasting, Elsevier, vol. 35(1), pages 371-389.
    21. Nicolas Huck, 2019. "Large data sets and machine learning: Applications to statistical arbitrage," Post-Print hal-02143971, HAL.
    22. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2018. "Bitcoin technical trading with artificial neural network," CARF F-Series CARF-F-430, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    23. Erdinc Akyildirim & Ahmet Goncu & Ahmet Sensoy, 2021. "Prediction of cryptocurrency returns using machine learning," Annals of Operations Research, Springer, vol. 297(1), pages 3-36, February.
    24. Akyildirim, Erdinc & Corbet, Shaen & Sensoy, Ahmet & Yarovaya, Larisa, 2020. "The impact of blockchain related name changes on corporate performance," Journal of Corporate Finance, Elsevier, vol. 65(C).
    25. Samitas, Aristeidis & Kampouris, Elias & Kenourgios, Dimitris, 2020. "Machine learning as an early warning system to predict financial crisis," International Review of Financial Analysis, Elsevier, vol. 71(C).
    26. Mona Shazly & Hassan Shazly, 1999. "Forecasting currency prices using a genetically evolved neural network architecture," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 5(1), pages 148-148, February.
    27. Jia‐Yen Huang & Jin‐Hao Liu, 2020. "Using social media mining technology to improve stock price forecast accuracy," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(1), pages 104-116, January.
    28. Paolo Giudici & Gloria Polinesi, 2021. "Crypto price discovery through correlation networks," Annals of Operations Research, Springer, vol. 299(1), pages 443-457, April.
    29. Corbet, Shaen & Cumming, Douglas J. & Lucey, Brian M. & Peat, Maurice & Vigne, Samuel A., 2020. "The destabilising effects of cryptocurrency cybercriminality," Economics Letters, Elsevier, vol. 191(C).
    30. Corbet, Shaen & Hou, Yang & Hu, Yang & Oxley, Les, 2020. "The influence of the COVID-19 pandemic on asset-price discovery: Testing the case of Chinese informational asymmetry," International Review of Financial Analysis, Elsevier, vol. 72(C).
    31. de la Horra, Luis P. & de la Fuente, Gabriel & Perote, Javier, 2019. "The drivers of Bitcoin demand: A short and long-run analysis," International Review of Financial Analysis, Elsevier, vol. 62(C), pages 21-34.
    32. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2018. "Bitcoin technical trading with artificial neural network," CARF F-Series CARF-F-441, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    33. Mensi, Walid & Sensoy, Ahmet & Vo, Xuan Vinh & Kang, Sang Hoon, 2020. "Impact of COVID-19 outbreak on asymmetric multifractality of gold and oil prices," Resources Policy, Elsevier, vol. 69(C).
    34. Carol Alexander & Jaehyuk Choi & Heungju Park & Sungbin Sohn, 2020. "BitMEX bitcoin derivatives: Price discovery, informational efficiency, and hedging effectiveness," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(1), pages 23-43, January.
    35. Corbet, Shaen & Hou, Yang (Greg) & Hu, Yang & Oxley, Les & Xu, Danyang, 2021. "Pandemic-related financial market volatility spillovers: Evidence from the Chinese COVID-19 epicentre," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 55-81.
    36. Hubáček, Ondřej & Šourek, Gustav & Železný, Filip, 2019. "Exploiting sports-betting market using machine learning," International Journal of Forecasting, Elsevier, vol. 35(2), pages 783-796.
    37. Masafumi Nakano & Akihiko Takahashi & Soichiro Takahashi, 2018. "Bitcoin Technical Trading with Articial Neural Network," CIRJE F-Series CIRJE-F-1090, CIRJE, Faculty of Economics, University of Tokyo.
    38. Hu, Yang & Hou, Yang (Greg) & Oxley, Les & Corbet, Shaen, 2021. "Does blockchain patent-development influence Bitcoin risk?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 70(C).
    39. Akyildirim, Erdinc & Corbet, Shaen & Katsiampa, Paraskevi & Kellard, Neil & Sensoy, Ahmet, 2020. "The development of Bitcoin futures: Exploring the interactions between cryptocurrency derivatives," Finance Research Letters, Elsevier, vol. 34(C).
    40. Justin Sirignano & Rama Cont, 2019. "Universal features of price formation in financial markets: perspectives from deep learning," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1449-1459, September.
    41. Ghoddusi, Hamed & Creamer, Germán G. & Rafizadeh, Nima, 2019. "Machine learning in energy economics and finance: A review," Energy Economics, Elsevier, vol. 81(C), pages 709-727.
    42. Shu, Min & Zhu, Wei, 2020. "Real-time prediction of Bitcoin bubble crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    43. Corbet, Shaen & Lucey, Brian & Urquhart, Andrew & Yarovaya, Larisa, 2019. "Cryptocurrencies as a financial asset: A systematic analysis," International Review of Financial Analysis, Elsevier, vol. 62(C), pages 182-199.
    44. Katsiampa, Paraskevi & Corbet, Shaen & Lucey, Brian, 2019. "High frequency volatility co-movements in cryptocurrency markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 62(C), pages 35-52.
    45. Corbet, Shaen & Larkin, Charles & Lucey, Brian, 2020. "The contagion effects of the COVID-19 pandemic: Evidence from gold and cryptocurrencies," Finance Research Letters, Elsevier, vol. 35(C).
    46. Goodell, John W., 2020. "COVID-19 and finance: Agendas for future research," Finance Research Letters, Elsevier, vol. 35(C).
    47. Conlon, Thomas & Corbet, Shaen & McGee, Richard J., 2020. "Are cryptocurrencies a safe haven for equity markets? An international perspective from the COVID-19 pandemic," Research in International Business and Finance, Elsevier, vol. 54(C).
    48. Philip, R., 2020. "Estimating permanent price impact via machine learning," Journal of Econometrics, Elsevier, vol. 215(2), pages 414-449.
    49. Akyildirim, Erdinc & Corbet, Shaen & Lucey, Brian & Sensoy, Ahmet & Yarovaya, Larisa, 2020. "The relationship between implied volatility and cryptocurrency returns," Finance Research Letters, Elsevier, vol. 33(C).
    50. Jan De Spiegeleer & Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2018. "Machine learning for quantitative finance: fast derivative pricing, hedging and fitting," Quantitative Finance, Taylor & Francis Journals, vol. 18(10), pages 1635-1643, October.
    51. Zhang, Guoqiang & Eddy Patuwo, B. & Y. Hu, Michael, 1998. "Forecasting with artificial neural networks:: The state of the art," International Journal of Forecasting, Elsevier, vol. 14(1), pages 35-62, March.
    52. Huck, Nicolas, 2019. "Large data sets and machine learning: Applications to statistical arbitrage," European Journal of Operational Research, Elsevier, vol. 278(1), pages 330-342.
    53. Sharif, Arshian & Aloui, Chaker & Yarovaya, Larisa, 2020. "COVID-19 pandemic, oil prices, stock market, geopolitical risk and policy uncertainty nexus in the US economy: Fresh evidence from the wavelet-based approach," International Review of Financial Analysis, Elsevier, vol. 70(C).
    54. Yarovaya, Larisa & Mirza, Nawazish & Abaidi, Jamila & Hasnaoui, Amir, 2021. "Human Capital efficiency and equity funds’ performance during the COVID-19 pandemic," International Review of Economics & Finance, Elsevier, vol. 71(C), pages 584-591.
    55. Katsiampa, Paraskevi & Corbet, Shaen & Lucey, Brian, 2019. "Volatility spillover effects in leading cryptocurrencies: A BEKK-MGARCH analysis," Finance Research Letters, Elsevier, vol. 29(C), pages 68-74.
    56. Feng Ma & Chao Liang & Yuanhui Ma & M.I.M. Wahab, 2020. "Cryptocurrency volatility forecasting: A Markov regime‐switching MIDAS approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(8), pages 1277-1290, December.
    57. Fan, Liwei & Pan, Sijia & Li, Zimin & Li, Huiping, 2016. "An ICA-based support vector regression scheme for forecasting crude oil prices," Technological Forecasting and Social Change, Elsevier, vol. 112(C), pages 245-253.
    58. Chen, Wei & Xu, Huilin & Jia, Lifen & Gao, Ying, 2021. "Machine learning model for Bitcoin exchange rate prediction using economic and technology determinants," International Journal of Forecasting, Elsevier, vol. 37(1), pages 28-43.
    59. Mahboubeh Faghih Mohammadi Jalali & Hanif Heidari, 2020. "Predicting changes in Bitcoin price using grey system theory," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-12, December.
    60. Corbet, Shaen & Lucey, Brian & Peat, Maurice & Vigne, Samuel, 2018. "Bitcoin Futures—What use are they?," Economics Letters, Elsevier, vol. 172(C), pages 23-27.
    61. Corbet, Shaen & Hou, Yang (Greg) & Hu, Yang & Larkin, Charles & Oxley, Les, 2020. "Any port in a storm: Cryptocurrency safe-havens during the COVID-19 pandemic," Economics Letters, Elsevier, vol. 194(C).
    62. Adamantios Ntakaris & Martin Magris & Juho Kanniainen & Moncef Gabbouj & Alexandros Iosifidis, 2018. "Benchmark dataset for mid‐price forecasting of limit order book data with machine learning methods," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 37(8), pages 852-866, December.
    63. Nakano, Masafumi & Takahashi, Akihiko & Takahashi, Soichiro, 2018. "Bitcoin technical trading with artificial neural network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 587-609.
    64. Wang, Minggang & Tian, Lixin & Zhou, Peng, 2018. "A novel approach for oil price forecasting based on data fluctuation network," Energy Economics, Elsevier, vol. 71(C), pages 201-212.
    65. Adcock, Robert & Gradojevic, Nikola, 2019. "Non-fundamental, non-parametric Bitcoin forecasting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kyriazis, Nikolaos & Papadamou, Stephanos & Tzeremes, Panayiotis & Corbet, Shaen, 2023. "Can cryptocurrencies provide a viable hedging mechanism for benchmark index investors?," Research in International Business and Finance, Elsevier, vol. 64(C).
    2. Yue, Yao & Li, Xuerong & Zhang, Dingxuan & Wang, Shouyang, 2021. "How cryptocurrency affects economy? A network analysis using bibliometric methods," International Review of Financial Analysis, Elsevier, vol. 77(C).
    3. Julien Chevallier & Dominique Guégan & Stéphane Goutte, 2021. "Is It Possible to Forecast the Price of Bitcoin?," Forecasting, MDPI, vol. 3(2), pages 1-44, May.
    4. Gradojevic, Nikola & Kukolj, Dragan & Adcock, Robert & Djakovic, Vladimir, 2023. "Forecasting Bitcoin with technical analysis: A not-so-random forest?," International Journal of Forecasting, Elsevier, vol. 39(1), pages 1-17.
    5. Flori, Andrea, 2019. "News and subjective beliefs: A Bayesian approach to Bitcoin investments," Research in International Business and Finance, Elsevier, vol. 50(C), pages 336-356.
    6. Helder Miguel Correia Virtuoso Sebastião & Paulo José Osório Rupino Da Cunha & Pedro Manuel Cortesão Godinho, 2021. "Cryptocurrencies and blockchain. Overview and future perspectives," International Journal of Economics and Business Research, Inderscience Enterprises Ltd, vol. 21(3), pages 305-342.
    7. Corbet, Shaen & Hou, Yang (Greg) & Hu, Yang & Oxley, Les, 2022. "The growth of oil futures in China: Evidence of market maturity through global crises," Energy Economics, Elsevier, vol. 114(C).
    8. Fan Fang & Carmine Ventre & Michail Basios & Leslie Kanthan & David Martinez-Rego & Fan Wu & Lingbo Li, 2022. "Cryptocurrency trading: a comprehensive survey," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-59, December.
    9. Corbet, Shaen & Hou, Yang (Greg) & Hu, Yang & Oxley, Les, 2022. "The influence of the COVID-19 pandemic on the hedging functionality of Chinese financial markets," Research in International Business and Finance, Elsevier, vol. 59(C).
    10. Fan Fang & Carmine Ventre & Michail Basios & Leslie Kanthan & Lingbo Li & David Martinez-Regoband & Fan Wu, 2020. "Cryptocurrency Trading: A Comprehensive Survey," Papers 2003.11352, arXiv.org, revised Jan 2022.
    11. Kyriazis, Nikolaos & Papadamou, Stephanos & Tzeremes, Panayiotis & Corbet, Shaen, 2023. "The differential influence of social media sentiment on cryptocurrency returns and volatility during COVID-19," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 307-317.
    12. Collings, David & Corbet, Shaen & Hou, Yang (Greg) & Hu, Yang & Larkin, Charles & Oxley, Les, 2022. "The effects of negative reputational contagion on international airlines: The case of the Boeing 737-MAX disasters," International Review of Financial Analysis, Elsevier, vol. 80(C).
    13. Corbet, Shaen & Hou, Yang (Greg) & Hu, Yang & Oxley, Les, 2021. "Volatility spillovers during market supply shocks: The case of negative oil prices," Resources Policy, Elsevier, vol. 74(C).
    14. Ren, Yi-Shuai & Ma, Chao-Qun & Kong, Xiao-Lin & Baltas, Konstantinos & Zureigat, Qasim, 2022. "Past, present, and future of the application of machine learning in cryptocurrency research," Research in International Business and Finance, Elsevier, vol. 63(C).
    15. Ahmed, Walid M.A., 2022. "Robust drivers of Bitcoin price movements: An extreme bounds analysis," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).
    16. Yarovaya, Larisa & Matkovskyy, Roman & Jalan, Akanksha, 2021. "The effects of a “black swan” event (COVID-19) on herding behavior in cryptocurrency markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 75(C).
    17. Bouteska, Ahmed & Abedin, Mohammad Zoynul & Hajek, Petr & Yuan, Kunpeng, 2024. "Cryptocurrency price forecasting – A comparative analysis of ensemble learning and deep learning methods," International Review of Financial Analysis, Elsevier, vol. 92(C).
    18. Bouri, Elie & Lau, Chi Keung Marco & Saeed, Tareq & Wang, Shixuan & Zhao, Yuqian, 2021. "On the intraday return curves of Bitcoin: Predictability and trading opportunities," International Review of Financial Analysis, Elsevier, vol. 76(C).
    19. Ashok, Shruti & Corbet, Shaen & Dhingra, Deepika & Goodell, John W. & Kumar, Satish & Yadav, Miklesh Prasad, 2022. "Are energy markets informationally smarter than equity markets? Evidence from the COVID-19 experience," Finance Research Letters, Elsevier, vol. 47(PB).
    20. Goodell, John W. & Ben Jabeur, Sami & Saâdaoui, Foued & Nasir, Muhammad Ali, 2023. "Explainable artificial intelligence modeling to forecast bitcoin prices," International Review of Financial Analysis, Elsevier, vol. 88(C).

    More about this item

    Keywords

    Cryptocurrency; Bitcoin futures; Machine learning; Covid-19; k-Nearest neighbors; Logistic regression; Naive bayes; Random forest; Support vector machine; Extreme gradient; Boosting;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • E50 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:cbsnow:2020_020. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CBS Library Research Registration Team (email available below). General contact details of provider: https://edirc.repec.org/data/incbsdk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.