{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T16:28:55Z","timestamp":1773246535432,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2012,1,23]],"date-time":"2012-01-23T00:00:00Z","timestamp":1327276800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Several measures of volatility have been developed in order to quantify the degree of uncertainty of an energy price series, which include historical volatility and price velocities, among others. This paper suggests using the permutation entropy, topological entropy and the modified permutation entropy as alternatives to measure volatility in energy markets. Simulated data show that these measures are more appropriate to quantify the uncertainty associated to a time series than those based on the standard deviation or other measures of dispersion. Finally, the proposed method is applied to some typical electricity markets: Nord Pool, Ontario, Omel and four Australian markets.<\/jats:p>","DOI":"10.3390\/e14010074","type":"journal-article","created":{"date-parts":[[2012,1,23]],"date-time":"2012-01-23T16:19:49Z","timestamp":1327335589000},"page":"74-91","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["A New Approach to Measure Volatility in Energy Markets"],"prefix":"10.3390","volume":"14","author":[{"given":"Mar\u00eda del Carmen","family":"Ruiz","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Universidad Polit\u00e9cnica de Cartagena, Cartagena 30202, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonio","family":"Guillam\u00f3n","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Universidad Polit\u00e9cnica de Cartagena, Cartagena 30202, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0952-4607","authenticated-orcid":false,"given":"Antonio","family":"Gabald\u00f3n","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Universidad Polit\u00e9cnica de Cartagena, Cartagena 30202, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,1,23]]},"reference":[{"key":"ref_1","unstructured":"Henning, B., Sloane, M., and de Leon, M. Natural gas and energy price volatility. American Gas Foundation 2003. Available online: http:\/\/www.gasfoundation.org\/ResearchStudies\/VolStudyCh5.pdf."},{"key":"ref_2","unstructured":"Newell, S., and Bhattacharyya, A. Cost-benefit analysis of replacing the NYISO\u2019s existing ICAP market with a forward capacity market. Available online: http:\/\/www.brattle.com\/_documents\/UploadLibrary\/Upload789.pdf."},{"key":"ref_3","unstructured":"Benini, M., Marracci, M., Pelacchi, P., and Venturini, A. (2002, January 25). Day-ahead market price volatility analysis in deregulated electricity markets. Proceedings of the IEEE Power Engineering Society Summer Meeting, Chicago, IL, USA."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"4739","DOI":"10.1016\/j.enpol.2007.04.006","article-title":"Electricity market price volatility: The case of Ontario","volume":"35","author":"Zareipour","year":"2007","journal-title":"Energy Policy"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1016\/S0301-4215(03)00130-7","article-title":"Deregulated power prices: Comparison of volatility","volume":"32","author":"Li","year":"2004","journal-title":"Energy Policy"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.physa.2005.02.062","article-title":"Volatility of power markets","volume":"335","author":"Simonsen","year":"2005","journal-title":"Phys. Stat. Mech. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/j.eneco.2005.11.003","article-title":"Oil and energy price volatility","volume":"29","author":"Regnier","year":"2007","journal-title":"Energ. Econ."},{"key":"ref_8","first-page":"105","article-title":"Measuring volatility in the nordic spot electricity market using recurrence quantification analysis","volume":"164","author":"Strozzi","year":"2008","journal-title":"Eur. Phys. J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"P11011","DOI":"10.1088\/1742-5468\/2006\/11\/P11011","article-title":"Entropy of the Nordic electricity market: Anomalous scaling, spikes, and mean reversion","volume":"11","author":"Perello","year":"2006","journal-title":"J. Stat. Mech. Theor. Exp."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1109\/TPWRS.2008.2006997","article-title":"Day ahead price forecasting of electricity markets by mutual information technique and cascaded neuro evolutionary algorithm","volume":"24","author":"Amjady","year":"2009","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"046217","DOI":"10.1103\/PhysRevE.70.046217","article-title":"Detecting dynamical changes in time series using the permutation entropy","volume":"70","author":"Cao","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s10072-008-0851-3","article-title":"Permutation entropy to detect vigilance changes and preictal states from scalp EEG in epileptic patients. A preliminary study","volume":"29","author":"Bruzzo","year":"2008","journal-title":"Neurol. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1901","DOI":"10.1080\/00207160902825184","article-title":"Estimating topological entropy from individual orbits","volume":"86","author":"Canovas","year":"2009","journal-title":"Int. J. Comput. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"043103","DOI":"10.1063\/1.3238256","article-title":"Permutations and time series analisys","volume":"19","author":"Canovas","year":"2009","journal-title":"Chaos"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1142\/S0219477511000375","article-title":"Using permutations to find structural changes in time series","volume":"10","author":"Canovas","year":"2011","journal-title":"Fluctuation and Noise Letters"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.88.174102","article-title":"Permutation entropy: A natural complexity measure for time series","volume":"88","author":"Bandt","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2690","DOI":"10.1088\/1674-1056\/18\/7\/011","article-title":"Fine-grained permutation entropy as a measure of natural complexity for time series","volume":"18","author":"Liu","year":"2009","journal-title":"Chin. Phys. B"},{"key":"ref_18","unstructured":"Nord Pool Spot. Available online: http:\/\/www.nordpoolspot.com."},{"key":"ref_19","unstructured":"Nord Pool Reservoir Data. Available online: http:\/\/www.nordpoolspot.com\/Market-data1\/Power-system-data\/Hydro-Reservoir\/."},{"key":"ref_20","unstructured":"Statistics Norway. Available online: http:\/\/www.ssb.no\/vannmag_en\/tab-01-en.shtml."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Bhattacharya, K., Bollen, M.H.J., and Daalder, J.E. (2001). Operation of Restructured Power Systems, Kluwer Academic Publishers.","DOI":"10.1007\/978-1-4615-1465-7"},{"key":"ref_22","unstructured":"Independent Electricity System Operator of Ontario Market. Available online: http:\/\/www.theimo.com\/imoweb\/marketdata\/marketData.asp."},{"key":"ref_23","unstructured":"Boletin Oficial del Estado (BOE) (Official State Gazette) Real Decreto (Royal Decree) 5\/2005 (in Spanish); BOE no. 62, 8832-8853 March 2005. Available online: http:\/\/www.boe.es."},{"key":"ref_24","unstructured":"Boletin Oficial del Estado (BOE) (Official State Gazette) Real Decreto (Royal Decree) 3\/2006 (in Spanish); BOE no. 150, 8015-8016, February 2006. Available online: http:\/\/www.boe.es."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Conejo, A. (2007, January 24\u201328). The electricity market of mainland Spain: A brief critical review. Proceedings of the IEEE Power Engineering Society General Meeting, Tampa, FL, USA.","DOI":"10.1109\/PES.2007.385712"},{"key":"ref_26","unstructured":"Electricity Market of Spain. Available online http:\/\/www.omie.es\/files\/me06cast.pdf."},{"key":"ref_27","unstructured":"Australian Energy Market Operator. Available online: http:\/\/www.aemo.com.au\/data\/price_demand.html."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/1\/74\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:48:37Z","timestamp":1760219317000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/1\/74"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,23]]},"references-count":27,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,1]]}},"alternative-id":["e14010074"],"URL":"https:\/\/doi.org\/10.3390\/e14010074","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1,23]]}}}