{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T21:32:57Z","timestamp":1773955977659,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2015,10,22]],"date-time":"2015-10-22T00:00:00Z","timestamp":1445472000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71201054"],"award-info":[{"award-number":["71201054"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["91224001"],"award-info":[{"award-number":["91224001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71433001"],"award-info":[{"award-number":["71433001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Fundamental Research Funds for the Central Universities in BUCT"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>For the modeling of complex and nonlinear crude oil price dynamics and movement, wavelet analysis can decompose the time series and produce multiple economically meaningful decomposition structures based on different assumptions of wavelet families and decomposition scale. However, the determination of the optimal model specification will critically affect the forecasting accuracy. In this paper, we propose a new wavelet entropy based approach to identify the optimal model specification and construct the effective wavelet entropy based forecasting models. The wavelet entropy algorithm is introduced to determine the optimal wavelet families and decomposition scale, that will produce the improved forecasting performance. Empirical studies conducted in the crude oil markets show that the proposed algorithm outperforms the benchmark model, in terms of conventional performance evaluation criteria for the model forecasting accuracy.<\/jats:p>","DOI":"10.3390\/e17107167","type":"journal-article","created":{"date-parts":[[2015,10,26]],"date-time":"2015-10-26T04:12:04Z","timestamp":1445832724000},"page":"7167-7184","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Wavelet Entropy Based Analysis and Forecasting of Crude Oil Price Dynamics"],"prefix":"10.3390","volume":"17","author":[{"given":"Yingchao","family":"Zou","sequence":"first","affiliation":[{"name":"School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China"},{"name":"College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lean","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kaijian","family":"He","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,10,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.econlet.2015.04.023","article-title":"Oil price forecastability and economic uncertainty","volume":"132","author":"Bekiros","year":"2015","journal-title":"Econ. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2761","DOI":"10.3390\/en7052761","article-title":"Crude Oil Spot Price Forecasting Based on Multiple Crude Oil Markets and Timeframes","volume":"7","author":"Deng","year":"2014","journal-title":"Energies"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"830","DOI":"10.1111\/ecin.12053","article-title":"Forecasting Crude Oil price Movements with Oil-Sensitive Stocks","volume":"52","author":"Chen","year":"2014","journal-title":"Econ. Inq."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"81","DOI":"10.5547\/ISSN0195-6574-EJ-Vol30-No3-4","article-title":"Modelling and Forecasting Oil Prices: The Role of Asymmetric Cycles","volume":"30","author":"Cuaresma","year":"2009","journal-title":"Energy J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1002\/jae.1159","article-title":"What Do We Learn from the Price of Crude Oil Futures?","volume":"25","author":"Alquist","year":"2010","journal-title":"J. Appl. Econom."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.enpol.2013.12.049","article-title":"Predicting oil price movements: A dynamic Artificial Neural Network approach","volume":"68","author":"Godarzi","year":"2014","journal-title":"Energy Policy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2623","DOI":"10.1016\/j.eneco.2008.05.003","article-title":"Forecasting crude oil price with an EMD-based neural network ensemble learning paradigm","volume":"30","author":"Yu","year":"2008","journal-title":"Energy Econ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1016\/j.dss.2012.11.009","article-title":"Prediction of movement direction in crude oil prices based on semi-supervised learning","volume":"55","author":"Shin","year":"2013","journal-title":"Decis. Support Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/j.petrol.2013.08.003","article-title":"Forecasting oil prices: Smooth transition and neural network augmented GARCH family models","volume":"109","author":"Bildirici","year":"2013","journal-title":"J. Pet. Sci. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"451","DOI":"10.2307\/3008764","article-title":"The Combination of Forecasts","volume":"20","author":"Bates","year":"1969","journal-title":"OR"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1142\/S0218348X12500120","article-title":"Study on the Fractal and Chaotic Features of the Shanghai Composite Index","volume":"20","author":"Wen","year":"2012","journal-title":"Fractals"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.physa.2015.01.035","article-title":"Asymmetric long-term autocorrelations in crude oil markets","volume":"424","author":"Alvarez","year":"2015","journal-title":"Physica A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"584","DOI":"10.1016\/j.eneco.2011.10.004","article-title":"A metric and topological analysis of determinism in the crude oil spot market","volume":"34","author":"Barkoulas","year":"2012","journal-title":"Energy Econ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1016\/j.physa.2014.07.036","article-title":"US stock market efficiency over weekly, monthly, quarterly and yearly time scales","volume":"413","author":"Rodriguez","year":"2014","journal-title":"Physica A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"690","DOI":"10.1080\/02664763.2014.980784","article-title":"Analyzing time-frequency relationship between oil price and exchange rate in Pakistan through wavelets","volume":"42","author":"Shahbaz","year":"2015","journal-title":"J. Appl. Stat."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.intfin.2014.11.011","article-title":"A wavelet-based nonlinear ARDL model for assessing the exchange rate pass-through to crude oil prices","volume":"34","author":"Jammazi","year":"2015","journal-title":"J. Int. Financ. Mark. Inst. Money"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1007\/s00181-014-0800-3","article-title":"Time-frequency relationship between share prices and exchange rates in India: Evidence from continuous wavelets","volume":"48","author":"Tiwari","year":"2015","journal-title":"Empir. Econ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1016\/j.energy.2012.07.055","article-title":"Crude oil price analysis and forecasting using wavelet decomposed ensemble model","volume":"46","author":"He","year":"2012","journal-title":"Energy"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"828","DOI":"10.1016\/j.eneco.2011.07.018","article-title":"Crude oil price forecasting: Experimental evidence from wavelet decomposition and neural network modeling","volume":"34","author":"Jammazi","year":"2012","journal-title":"Energy Econ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1507","DOI":"10.1016\/j.eneco.2010.08.006","article-title":"Forecasting oil price trends using wavelets and hidden Markov models","volume":"32","author":"Legey","year":"2010","journal-title":"Energy Econ."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/j.chaos.2004.11.015","article-title":"Wavelet-Based Prediction of Oil Prices","volume":"25","author":"Yousefi","year":"2005","journal-title":"Chaos Solitons Fractals"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1080\/15567249.2011.557685","article-title":"A Novel Hybrid Forecasting Method Using GRNN Combined With Wavelet Transform and a GARCH Model","volume":"10","author":"Zhang","year":"2015","journal-title":"Energy Sources B"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.resourpol.2013.10.005","article-title":"An improved wavelet, \u00c4\u00edARIMA approach for forecasting metal prices","volume":"39","author":"Kriechbaumer","year":"2014","journal-title":"Resour. Pol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.csda.2014.02.024","article-title":"Interest rate spreads and output: A time scale decomposition analysis using wavelets","volume":"76","author":"Gallegati","year":"2014","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"932","DOI":"10.1103\/PhysRevE.57.932","article-title":"Time-frequency analysis of electroencephalogram series. III. Wavelet packets and information cost function","volume":"57","author":"Blanco","year":"1998","journal-title":"Phys. Rev. E"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1109\/18.119732","article-title":"Entropy-Based Algorithms for Best Basis Selection","volume":"38","author":"Coifman","year":"1992","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2768","DOI":"10.3390\/e16052768","article-title":"Market Efficiency, Roughness and Long Memory in PSI20 Index Returns: Wavelet and Entropy Analysis","volume":"16","author":"Pascoal","year":"2014","journal-title":"Entropy"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1142\/S0129183107010322","article-title":"Dynamics of avalanche activities in financial markets","volume":"18","author":"Kim","year":"2007","journal-title":"Int. J. Money Phys. C"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1016\/j.compbiomed.2013.01.022","article-title":"Improved wavelet entropy calculation with window functions and its preliminary application to study intracranial pressure","volume":"43","author":"Xu","year":"2013","journal-title":"Comput. Biol. Med."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1109\/TPWRD.2012.2220987","article-title":"Wavelet Singular Entropy-Based Islanding Detection in Distributed Generation","volume":"28","author":"Samui","year":"2013","journal-title":"IEEE Trans. Power Deliv."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"6542","DOI":"10.1016\/j.energy.2011.09.010","article-title":"A novel seasonal decomposition based least squares support vector regression ensemble learning approach for hydropower consumption forecasting in China","volume":"36","author":"Wang","year":"2011","journal-title":"Energy"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"936","DOI":"10.1016\/j.eneco.2011.03.012","article-title":"Multiscale entropy analysis of crude oil price dynamics","volume":"33","author":"Martina","year":"2011","journal-title":"Energy Econ."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.enpol.2011.10.057","article-title":"Efficiency of crude oil markets: Evidences from informational entropy analysis","volume":"41","author":"Rodriguez","year":"2012","journal-title":"Energy Policy"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.cnsns.2014.08.038","article-title":"Quantifying complexity of financial short-term time series by composite multiscale entropy measure","volume":"22","author":"Niu","year":"2015","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2921","DOI":"10.1007\/s11071-014-1636-2","article-title":"Weighted multiscale permutation entropy of financial time series","volume":"78","author":"Yin","year":"2014","journal-title":"Nonlinear Dyn."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1274","DOI":"10.3390\/e14071274","article-title":"Discrete Wavelet Entropy Aided Detection of Abrupt Change: A Case Study in the Haihe River Basin, China","volume":"14","author":"Sang","year":"2012","journal-title":"Entropy"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.jimonfin.2004.10.003","article-title":"Multiscale Systematic Risk","volume":"24","author":"Gencay","year":"2005","journal-title":"J. Int. Money Financ."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Gen\u00e7ay, R., Sel\u00e7uk, F., and Whitcher, B. (2002). An Introduction to Wavelets and Other Filtering Methods in Finance and Economics, Academic Press.","DOI":"10.1016\/B978-012279670-8.50004-5"},{"key":"ref_40","unstructured":"Brock, W.A., Hsieh, D.A., and LeBaron, B.D. (1991). Nonlinear Dynamics, Chaos, and Instability : Statistical Theory and Economic Evidence, MIT Press."},{"key":"ref_41","first-page":"1","article-title":"Testing the Assumption of Linearity","volume":"3","author":"Panagiotidis","year":"2002","journal-title":"Econ. Bull."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1111\/j.1467-9892.1982.tb00339.x","article-title":"Testing for Gaussianity and Linearity of a Stationary Time Series","volume":"3","author":"Hinich","year":"1982","journal-title":"J. Time Ser. Anal."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"41","DOI":"10.2307\/2331150","article-title":"Implications of Nonlinear Dynamics for Financial Risk Management","volume":"28","author":"Hsieh","year":"1993","journal-title":"J. Financ. Quant. Anal."},{"key":"ref_44","unstructured":"Hamilton, J.D. (2013). Routledge Handbook of Major Events in Economic History, Taylor and Francis Group."},{"key":"ref_45","unstructured":"Group, W.B. (2015). Global Economic Prospects, January 2015: Having Fiscal Space and Using It, World Bank."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.enpol.2013.12.052","article-title":"Testing the evolution of crude oil market efficiency: Data have the conn","volume":"68","author":"Zhang","year":"2014","journal-title":"Energy Policy"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.jeconom.2005.07.014","article-title":"Using Out-Of-Sample Mean Squared Prediction Errors to Test the Martingale Difference Hypothesis","volume":"135","author":"Clark","year":"2006","journal-title":"J. Econom."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.jeconom.2006.05.023","article-title":"Approximately Normal Tests for Equal Predictive Accuracy in Nested Models","volume":"138","author":"Clark","year":"2007","journal-title":"J. Econom."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/10\/7167\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:50:38Z","timestamp":1760215838000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/10\/7167"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,22]]},"references-count":48,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2015,10]]}},"alternative-id":["e17107167"],"URL":"https:\/\/doi.org\/10.3390\/e17107167","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10,22]]}}}