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The Continuous Wavelet Transform: A Primer

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Abstract

Wavelet analysis is becoming more popular in the Economics discipline. Until recently, most works have made use of tools associated with the Discrete Wavelet Transform. However, after 2005, there has been a growing body of work in Economics and Finance that makes use of the Continuous Wavelet Transform tools. In this article, we give a self-contained summary on the most relevant theoretical results associated with the Continuous Wavelet Transform, the Cross-Wavelet Transform, the Wavelet Coherency and the Wavelet Phase-Difference. We describe how the transforms are usually implemented in practice and provide some examples. We also introduce the Economists to a new class of analytic wavelets, the Generalized Morse Wavelets, which have some desirable properties and provide an alternative to the Morlet Wavelet. Finally, we provide a user friendly toolbox which will allow any researcher to replicate our results and to use it in his/her own research.

Suggested Citation

  • Luís Francisco Aguiar & Maria Joana Soares, 2010. "The Continuous Wavelet Transform: A Primer," NIPE Working Papers 23/2010, NIPE - Universidade do Minho.
  • Handle: RePEc:nip:nipewp:23/2010
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    Cited by:

    1. Lubos Hanus & Lukas Vacha, 2015. "Business cycle synchronization of the Visegrad Four and the European Union," Working Papers IES 2015/19, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Jul 2015.
    2. Trezzi, Riccardo, 2013. "A wavelet analysis of international risk-sharing," Economics Letters, Elsevier, vol. 118(2), pages 330-333.
    3. KRAVETS Tetyana & LIASHENKO Olena, 2014. "The Synchronization Effects Of Stock Indices Dynamics In The Multifractal Analysis Using The Wavelet Technology," Revista Economica, Lucian Blaga University of Sibiu, Faculty of Economic Sciences, vol. 66(2), pages 41-57.
    4. Jusoh, Hashim & Bacha, Obiyathulla & Masih, Abul Mansur M., 2014. "Multi-scale Lead-Lag Relationship between the Stock and Futures Markets: Malaysia as a Case Study," MPRA Paper 56954, University Library of Munich, Germany.
    5. repec:eee:phsmap:v:486:y:2017:i:c:p:933-946 is not listed on IDEAS
    6. Boako, Gideon & Alagidede, Paul, 2017. "Co-movement of Africa’s equity markets: Regional and global analysis in the frequency–time domains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 359-380.
    7. Luís Francisco Aguiar & Teresa Maria Rodrigues & Maria Joana Soares, 2012. "Oil Shocks and the Euro as an Optimum Currency Area," NIPE Working Papers 07/2012, NIPE - Universidade do Minho.
    8. Aguiar-Conraria, Luís & Martins, Manuel M.F. & Soares, Maria Joana, 2012. "The yield curve and the macro-economy across time and frequencies," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1950-1970.
    9. Emre Kahraman & Gazanfer Unal, 2016. "Multiple Wavelet Coherency Analysis and Forecasting of Metal Prices," Papers 1602.01960, arXiv.org.
    10. Maissa Elmrabet & Boulila Ghazi, 2018. "Causality deficit-inflation : wavelet transform," Working Papers hal-01941464, HAL.
    11. Bouoiyour, Jamal & Selmi, Refk, 2014. "What Bitcoin Looks Like?," MPRA Paper 58091, University Library of Munich, Germany.
    12. repec:wsi:ijfexx:v:04:y:2017:i:01:n:s2424786317500074 is not listed on IDEAS
    13. Kabir, Sarkar Humayun & Masih, Mansur, 2014. "Dynamic Integration of Domestic Equity Price, Foreign Equity Price and Macroeconomic Indicators: Evidence from Malaysia," MPRA Paper 57007, University Library of Munich, Germany.
    14. Harald Schmidbauer & Angi Rosch & Erhan Uluceviz, 2016. "Frequency aspects of information transmission in a network of three Western equity markets," Koç University-TUSIAD Economic Research Forum Working Papers 1616, Koc University-TUSIAD Economic Research Forum.
    15. Rua, António & Nunes, Luis C., 2012. "A wavelet-based assessment of market risk: The emerging markets case," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(1), pages 84-92.
    16. repec:eee:reveco:v:55:y:2018:i:c:p:285-294 is not listed on IDEAS
    17. Angi Roesch & Harald Schmidbauer & Erhan Uluceviz, 2014. "Frequency Aspects Of Information Transmission In Networks Of Equity Markets," EcoMod2014 7200, EcoMod.
    18. Caraiani, Petre, 2012. "Stylized facts of business cycles in a transition economy in time and frequency," Economic Modelling, Elsevier, vol. 29(6), pages 2163-2173.
    19. Aguiar-Conraria, LuI´s & Joana Soares, Maria, 2011. "Business cycle synchronization and the Euro: A wavelet analysis," Journal of Macroeconomics, Elsevier, vol. 33(3), pages 477-489, September.
    20. repec:wsi:afexxx:v:10:y:2015:i:01:n:s2010495215500025 is not listed on IDEAS
    21. Habimana, Olivier, 2016. "Oil price, exchange rate and consumer price co-movement: A continuous-wavelet analysis," MPRA Paper 71886, University Library of Munich, Germany.

    More about this item

    Keywords

    Economic cycles; ContinuousWavelet Transform; Cross-Wavelet Transform; Wavelet Coherency; Wavelet Phase-Difference; The Great Moderation.;

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