IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v40y2009i3p1118-1126.html
   My bibliography  Save this article

Relationship of d-dimensional continuous multi-scale wavelet shrinkage with integro-differential equations

Author

Listed:
  • Liu, Guojun
  • Feng, Xiangchu
  • Li, Min

Abstract

The goal of this paper is to extend the results of Didas and Weickert [Didas, S, Weickert, J. Integrodifferential equations for continuous multi-scale wavelet shrinkage. Inverse Prob Imag 2007;1:47–62.] to d-dimensional (d⩾1) case. Firstly, we relate a d-dimensional continuous mother wavelet ψ(x) with a fast decay and n vanishing moments to the sum of the order partial derivative of a group of functions θk(x)(∣k∣=n) with fast decay, which also makes wavelet transform equal to a sum of smoothed partial derivative operators. Moreover, d-dimensional continuous wavelet transform can be explained as a weighted average of pseudo-differential equations, too. For d=1, our results are completely same as Didas and Weickert (2007), but for d>1, it is different from the type of one variable. Finally, we exploit the reason with an example of 2-dimensional and 3-dimensional Mexican hat wavelet.

Suggested Citation

  • Liu, Guojun & Feng, Xiangchu & Li, Min, 2009. "Relationship of d-dimensional continuous multi-scale wavelet shrinkage with integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1118-1126.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1118-1126
    DOI: 10.1016/j.chaos.2007.08.066
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907007011
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.08.066?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Huang, Yongdong & Cheng, Zhengxing & Yang, Jianwei, 2007. "Design of compactly supported trivariate orthogonal wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1440-1449.
    2. Yousefi, Shahriar & Weinreich, Ilona & Reinarz, Dominik, 2005. "Wavelet-based prediction of oil prices," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 265-275.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nowotarski, Jakub & Tomczyk, Jakub & Weron, Rafał, 2013. "Robust estimation and forecasting of the long-term seasonal component of electricity spot prices," Energy Economics, Elsevier, vol. 39(C), pages 13-27.
    2. Singh, Sarbjit & Parmar, Kulwinder Singh & Kumar, Jatinder & Makkhan, Sidhu Jitendra Singh, 2020. "Development of new hybrid model of discrete wavelet decomposition and autoregressive integrated moving average (ARIMA) models in application to one month forecast the casualties cases of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    3. Shalini, Velappan & Prasanna, Krishna, 2016. "Impact of the financial crisis on Indian commodity markets: Structural breaks and volatility dynamics," Energy Economics, Elsevier, vol. 53(C), pages 40-57.
    4. Joanna Janczura & Rafał Weron, 2012. "Efficient estimation of Markov regime-switching models: An application to electricity spot prices," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(3), pages 385-407, July.
    5. Sun, Lei & Zhang, Xiaozhong, 2009. "A note on biorthogonality of the scaling functions with arbitrary matrix dilation factor," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 711-715.
    6. Bekiros, Stelios & Marcellino, Massimiliano, 2013. "The multiscale causal dynamics of foreign exchange markets," Journal of International Money and Finance, Elsevier, vol. 33(C), pages 282-305.
    7. Drachal, Krzysztof, 2016. "Forecasting spot oil price in a dynamic model averaging framework — Have the determinants changed over time?," Energy Economics, Elsevier, vol. 60(C), pages 35-46.
    8. Jammazi, Rania & Aloui, Chaker, 2012. "Crude oil price forecasting: Experimental evidence from wavelet decomposition and neural network modeling," Energy Economics, Elsevier, vol. 34(3), pages 828-841.
    9. Huang, Yongdong & Lei, Chongmin & Yang, Miao, 2009. "The construction of a class of trivariate nonseparable compactly supported orthogonal wavelets," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1530-1537.
    10. Haven, Emmanuel & Liu, Xiaoquan & Ma, Chenghu & Shen, Liya, 2009. "Revealing the implied risk-neutral MGF from options: The wavelet method," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 692-709, March.
    11. Bjørn Gunnar Hansen & Yushu Li, 2017. "An Analysis of Past World Market Prices of Feed and Milk and Predictions for the Future," Agribusiness, John Wiley & Sons, Ltd., vol. 33(2), pages 175-193, April.
    12. Haven, Emmanuel & Liu, Xiaoquan & Shen, Liya, 2012. "De-noising option prices with the wavelet method," European Journal of Operational Research, Elsevier, vol. 222(1), pages 104-112.
    13. Vacha, Lukas & Barunik, Jozef, 2012. "Co-movement of energy commodities revisited: Evidence from wavelet coherence analysis," Energy Economics, Elsevier, vol. 34(1), pages 241-247.
    14. Korotin, Vladimir & Dolgonosov, Maxim & Popov, Victor & Korotina, Olesya & Korolkova, Inna, 2019. "The Ukrainian crisis, economic sanctions, oil shock and commodity currency: Analysis based on EMD approach," Research in International Business and Finance, Elsevier, vol. 48(C), pages 156-168.
    15. He, Kaijian & Yu, Lean & Lai, Kin Keung, 2012. "Crude oil price analysis and forecasting using wavelet decomposed ensemble model," Energy, Elsevier, vol. 46(1), pages 564-574.
    16. Huang, Shupei & An, Haizhong & Gao, Xiangyun & Huang, Xuan, 2015. "Identifying the multiscale impacts of crude oil price shocks on the stock market in China at the sector level," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 13-24.
    17. Fan, Ying & Liang, Qiang & Wei, Yi-Ming, 2008. "A generalized pattern matching approach for multi-step prediction of crude oil price," Energy Economics, Elsevier, vol. 30(3), pages 889-904, May.
    18. Jesús Molina‐Muñoz & Andrés Mora‐Valencia & Javier Perote, 2024. "Predicting carbon and oil price returns using hybrid models based on machine and deep learning," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 31(2), June.
    19. Kaijian He & Kin Keung Lai & Guocheng Xiang, 2012. "Portfolio Value at Risk Estimate for Crude Oil Markets: A Multivariate Wavelet Denoising Approach," Energies, MDPI, vol. 5(4), pages 1-26, April.
    20. Xiao Jing Cai & Zheng Fang & Youngho Chang & Shuairu Tian & Shigeyuki Hamori, 2020. "Co-movements in commodity markets and implications in diversification benefits," Empirical Economics, Springer, vol. 58(2), pages 393-425, February.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1118-1126. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.