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Approaches and tools usually applied to characterize standard stocks have been applied to the digital ones. Among these tools is the identification of processes of market fluctuations. Being interesting stochastic processes, the usual statistical methods are appropriate tools for their reconstruction. There, besides chance, the description of a behavioural component shall be present whenever a deterministic pattern is ever found. Markov approaches are at the leading edge of this endeavour. In this paper, Markov chains of orders one to eight are considered as a way to forecast the dynamics of three major cryptocurrencies. It is accomplished using an empirical basis of intra-day returns. Besides forecasting, we investigate the existence of eventual long-memory components in each of those stochastic processes. Results show that predictions obtained from using the empirical probabilities are better than random choices.<\/jats:p>","DOI":"10.1007\/s10614-023-10512-1","type":"journal-article","created":{"date-parts":[[2023,12,24]],"date-time":"2023-12-24T14:01:55Z","timestamp":1703426515000},"page":"2509-2521","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Reconstructing Cryptocurrency Processes via Markov Chains"],"prefix":"10.1007","volume":"64","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6993-7043","authenticated-orcid":false,"given":"Tanya","family":"Ara\u00fajo","sequence":"first","affiliation":[]},{"given":"Paulo","family":"Barbosa","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,12,24]]},"reference":[{"key":"10512_CR1","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.econlet.2015.02.029","volume":"484","author":"AF Bariviera","year":"2017","unstructured":"Bariviera, A. F., Basgall, M. J., Hasperue, W., & Naiouf, M. (2017). Some stylized facts of the Bitcoin market. Physica A: Statistical Mechanics and Its Applications, 484, 82\u201390. https:\/\/doi.org\/10.1016\/j.econlet.2015.02.029","journal-title":"Physica A: Statistical Mechanics and Its Applications"},{"issue":"2","key":"10512_CR2","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1111\/j.1540-6288.2010.00244.x","volume":"45","author":"D Baur","year":"2010","unstructured":"Baur, D., & Lucey, B. M. (2010). Is gold a hedge or a safe haven? An analysis of stocks, bonds and gold. Financial Review, 45(2), 217\u201329. https:\/\/doi.org\/10.1111\/j.1540-6288.2010.00244.x","journal-title":"Financial Review"},{"key":"10512_CR3","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/j.econlet.2018.02.010","volume":"167","author":"ET Cheah","year":"2018","unstructured":"Cheah, E. T., Mishra, T., Parhi, M., & Zhang, Z. (2018). Long memory interdependency and inefficiency in bitcoin markets. Economics Letters, 167, 18\u201325.","journal-title":"Economics Letters"},{"key":"10512_CR4","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1016\/j.econlet.2018.01.00","volume":"165","author":"S Corbet","year":"2018","unstructured":"Corbet, S., Meegan, A., Larkin, C., Lucey, B., & Yarovaya, L. (2018). Exploring the dynamic relationships between cryptocurrencies and other financial assets. Economics Letters, 165, 28\u201334. https:\/\/doi.org\/10.1016\/j.econlet.2018.01.00","journal-title":"Economics Letters"},{"key":"10512_CR5","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1016\/j.physa.2020.124155","volume":"550","author":"CR Cunha","year":"2020","unstructured":"Cunha, C. R., & Silva, R. (2020). Relevant Stylized Facts about Bitcoin: Fluctuations, First Return Probability, and Natural Phenomena. 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