{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:47:35Z","timestamp":1760240855480,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,10,18]],"date-time":"2019-10-18T00:00:00Z","timestamp":1571356800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>We implement hidden Markov models (HMMs) and hidden semi-Markov models (HSMMs) on Bitcoin\/US dollar (BTC\/USD) with the aim of market phase detection. We make analogous comparisons to Standard and Poor\u2019s 500 (S and P 500), a benchmark traditional stock index and a protagonist of several studies in finance. Popular labels given to market phases are \u201cbull\u201d, \u201cbear\u201d, \u201ccorrection\u201d, and \u201crally\u201d. In the first part, we fit HMMs and HSMMs and look at the evolution of hidden state parameters and state persistence parameters over time to ensure that states are correctly classified in terms of market phase labels. We conclude that our modelling approaches yield positive results in both BTC\/USD and the S and P 500, and both are best modelled via four-state HSMMs. However, the two assets show different regime volatility and persistence patterns\u2014BTC\/USD has volatile bull and bear states and generally weak state persistence, while the S and P 500 shows lower volatility on the bull states and stronger state persistence. In the second part, we put our models to the test of detecting different market phases by devising investment strategies that aim to be more profitable on unseen data in comparison to a buy-and-hold approach. In both cases, for select investment strategies, four-state HSMMs are also the most profitable and significantly outperform the buy-and-hold strategy.<\/jats:p>","DOI":"10.3390\/info10100322","type":"journal-article","created":{"date-parts":[[2019,10,18]],"date-time":"2019-10-18T11:24:15Z","timestamp":1571397855000},"page":"322","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Analysis and Comparison of Bitcoin and S and P 500 Market Features Using HMMs and HSMMs \u2020"],"prefix":"10.3390","volume":"10","author":[{"given":"David","family":"Suda","sequence":"first","affiliation":[{"name":"Faculty of Science, University of Malta, Msida 2080, Malta"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7290-2025","authenticated-orcid":false,"given":"Luke","family":"Spiteri","sequence":"additional","affiliation":[{"name":"Faculty of Science, University of Malta, Msida 2080, Malta"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Suda, D., and Spiteri, L. (2019). Comparing market phase features for cryptocurrency and benchmark stock index using HMM and HSMM filtering. Lecture Notes in Business Information Processing, Springer.","DOI":"10.1007\/978-3-030-36691-9_17"},{"key":"ref_2","unstructured":"Nakamoto, S. (2019, October 17). Bitcoin: A Peer-to-Peer Electronic Cash System. Available online: www.bitcoin.org."},{"key":"ref_3","unstructured":"ECB Crypto-Assets Task Force (European Central Bank) (2019). Crypto-Assets: Implications for Financial Stability, Monetary Policy, and Payments and Market Infrastructures, European Central Bank. Available online: https:\/\/www.ecb.europa.eu\/pub\/pdf\/scpops\/ecb.op223~3ce14e986c.en.pdf."},{"key":"ref_4","unstructured":"Glaser, F., Zimmermann, K., Haferkorn, M., Weber, M.C., and Siering, M. (2014, January 9\u201311). Bitcoin\u2014Asset or currency? Revealing users\u2019 hidden intentions. Proceedings of the 22nd European Conference of Information Systems, Tel Aviv, Israel."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1080\/07421222.2018.1440774","article-title":"How does social media impact Bitcoin value? A test of the silent majority hypothesis","volume":"35","author":"Mai","year":"2015","journal-title":"J. Manag. Inf. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Yermack, D. (2015). Is Bitcoin a real currency?. The Handbook of Digital Currency, Elsevier. [1st ed.].","DOI":"10.1016\/B978-0-12-802117-0.00002-3"},{"key":"ref_7","first-page":"56","article-title":"Bitcoin: The promise and limmits of private innovation in monetary and payment systems","volume":"4","author":"Beer","year":"2014","journal-title":"Monet. Policy Econ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1080\/13504851.2014.916379","article-title":"Bitcoin as an investment or speculative vehicle? A first look","volume":"22","author":"Baek","year":"2015","journal-title":"Appl. Econ. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Chan, S., Chu, J., Nadarajah, S., and Osterrieder, J. (2017). A statistical analysis of cryptocurrencies. J. Risk Financ. Manag., 10.","DOI":"10.3390\/jrfm10020012"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.frl.2017.10.012","article-title":"Bitcoin, gold and the dollar\u2014A replication and extension","volume":"25","author":"Baur","year":"2018","journal-title":"Financ. Res. Lett."},{"key":"ref_11","first-page":"2016","article-title":"On the return-volatility relationship in the Bitcoin market around the price crash of 2013","volume":"11","author":"Bouri","year":"2018","journal-title":"Econstor Econ. Discuss. Pap."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Chu, J., Chan, S., Nadarajah, S., and Osterrieder, J. (2017). GARCH modelling of cyprtocurrencies. J. Risk Financ. Manag., 10.","DOI":"10.2139\/ssrn.3047027"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.econlet.2017.06.023","article-title":"Volatility estimation for Bitcoin, a comparison of GARCH models","volume":"158","author":"Katsiampa","year":"2017","journal-title":"Econ. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1108\/JRF-07-2017-0115","article-title":"Value-at-risk and related measures for the Bitcoin","volume":"19","author":"Stavroyiannis","year":"2018","journal-title":"J. Risk Financ."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kodama, O., Pichl, L., and Kaizoji, T. (2017, January 22\u201324). Regime change and trend prediction for Bitcoin time series data. Proceedings of the CBU International Conference on Innovations in Science and Education 2017, Prague, Czech Republic.","DOI":"10.12955\/cbup.v5.954"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ardia, D., Bluteau, K., and Reude, M. (2018). Regime changes in Bitcoin GARCH volatility dynamics. Financ. Res. Lett., in press.","DOI":"10.1016\/j.frl.2018.08.009"},{"key":"ref_17","unstructured":"Bonello, A., and Suda, D. (2018, January 24\u201326). Volatility regime analysis of Bitcoin price dynamics using Markov switching GARCH models. Proceedings of the 22nd European Simulation and Modelling Conference 2018, Ghent, Belgium."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1002\/for.2524","article-title":"Predicting cryptocurrencies using sparse non-Gaussian state space models","volume":"37","author":"Huber","year":"2018","journal-title":"J. Forecast"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/j.frl.2018.03.018","article-title":"Bayesian changepoint analysis of Bitcoin returns","volume":"27","author":"Thies","year":"2018","journal-title":"Financ. Res. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1002\/(SICI)1099-1255(199805\/06)13:3<217::AID-JAE476>3.0.CO;2-V","article-title":"Stylized facts of daily return series and the hidden Markov model","volume":"13","year":"1998","journal-title":"J. Appl. Econometr."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"67","DOI":"10.2307\/20076016","article-title":"Some properties of absolute return: An alternative measure of risk","volume":"40","author":"Granger","year":"1995","journal-title":"Annales d\u2019Economic et de Statistique"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Nguyen, N. (2018). Hidden Markov Model for Stock Trading. Int. J. Financ. Stud., 6.","DOI":"10.3390\/ijfs6020036"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2192","DOI":"10.1016\/j.csda.2006.07.021","article-title":"Stylized facts of financial time series and hidden semi-Markov models","volume":"51","author":"Bulla","year":"2007","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.pacfin.2017.06.007","article-title":"Decoding Chinese stock market returns: Three-state hidden semi-Markov model","volume":"44","author":"Liu","year":"2017","journal-title":"Pac.-Basin Financ. J."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zucchini, W., MacDonald, I.L., and Langrock, R. (2016). Hidden Markov Models for Time Series: An introduction Using R, Chapman & Hall\/CRC. [2nd ed.].","DOI":"10.1201\/b20790"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1198\/1061860032030","article-title":"Estimating hidden semi-Markov chains from discrete sequences","volume":"12","year":"2003","journal-title":"J. Comp. Graph. Stat."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1109\/TIT.1967.1054010","article-title":"Error bounds for convolutional codes and an asymptotically optimal decoding algorithm","volume":"13","author":"Viterbi","year":"1967","journal-title":"IEEE Trans. Inf. Thepry"},{"key":"ref_28","unstructured":"Harte, D. (2019, March 12). R Package \u2019HiddenMarkov\u2019. Available online: http:\/\/homepages.maxnet.co.nz\/davidharte\/SSLIB\/."},{"key":"ref_29","unstructured":"Bulla, J., and Bulla, I. (2019, March 12). hsmm: Hidden semi-Markov Models. Available online: http:\/\/CRAN.R-project.org\/package=hsmm."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/10\/10\/322\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:27:33Z","timestamp":1760189253000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/10\/10\/322"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,18]]},"references-count":29,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2019,10]]}},"alternative-id":["info10100322"],"URL":"https:\/\/doi.org\/10.3390\/info10100322","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2019,10,18]]}}}