IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i5p844-d361975.html
   My bibliography  Save this article

A New Wavelet Tool to Quantify Non-Periodicity of Non-Stationary Economic Time Series

Author

Listed:
  • Vicente J. Bolós

    (Dpto. Matemáticas para la Economía y la Empresa, Facultad de Economía, Universidad de Valencia, Avda. Tarongers s/n, 46022 Valencia, Spain)

  • Rafael Benítez

    (Dpto. Matemáticas para la Economía y la Empresa, Facultad de Economía, Universidad de Valencia, Avda. Tarongers s/n, 46022 Valencia, Spain)

  • Román Ferrer

    (Dpto. Economía Financiera y Actuarial, Facultad de Economía, Universidad de Valencia, Avda. Tarongers s/n, 46022 Valencia, Spain)

Abstract

We introduce a new wavelet tool, the windowed scale index, to study the degree of non-periodicity of time series. The windowed scale index is based on some recently defined tools, such as the windowed scalogram and the scale index. This novel measure is appropriate for non-stationary time series whose characteristics change over time and, therefore, it can be applied to a wide variety of disciplines. Furthermore, we revise the concept of the scale index and pose a theoretical problem: it is known that if the scale index of a function is not zero then it is non-periodic, but if the scale index of a function is zero, then it is not proved that it has to be periodic. This problem is solved for the particular case of the Haar wavelet, reinforcing the interpretation of the windowed scale index as a useful tool to quantify non-periodicity. In addition, the applicability of this wavelet-based measure is illustrated through several examples, including an economic application which compares the non-periodicity of two major commodities in the world economy, such as crude oil and gold. Finally, we discuss the relationship between non-periodicity and unpredictability, comparing the windowed scale index with the sample entropy.

Suggested Citation

  • Vicente J. Bolós & Rafael Benítez & Román Ferrer, 2020. "A New Wavelet Tool to Quantify Non-Periodicity of Non-Stationary Economic Time Series," Mathematics, MDPI, vol. 8(5), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:844-:d:361975
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/5/844/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/5/844/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Baur, Dirk G. & McDermott, Thomas K., 2010. "Is gold a safe haven? International evidence," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1886-1898, August.
    2. Dirk G. Baur & Brian M. Lucey, 2010. "Is Gold a Hedge or a Safe Haven? An Analysis of Stocks, Bonds and Gold," The Financial Review, Eastern Finance Association, vol. 45(2), pages 217-229, May.
    3. Ratti, Ronald A & Vespignani, Joaquin L., 2012. "Why are crude oil prices high when global activity is weak?," MPRA Paper 43777, University Library of Munich, Germany.
    4. Ciner, Cetin & Gurdgiev, Constantin & Lucey, Brian M., 2013. "Hedges and safe havens: An examination of stocks, bonds, gold, oil and exchange rates," International Review of Financial Analysis, Elsevier, vol. 29(C), pages 202-211.
    5. Miguel Henry & George Judge, 2019. "Permutation Entropy and Information Recovery in Nonlinear Dynamic Economic Time Series," Econometrics, MDPI, vol. 7(1), pages 1-16, March.
    6. Ratti, Ronald A. & Vespignani, Joaquin L., 2013. "Why are crude oil prices high when global activity is weak?," Economics Letters, Elsevier, vol. 121(1), pages 133-136.
    7. Aguilera, Roberto F. & Radetzki, Marian, 2017. "The synchronized and exceptional price performance of oil and gold: Explanations and prospects," Resources Policy, Elsevier, vol. 54(C), pages 81-87.
    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. Aye, Goodness & Gupta, Rangan & Hammoudeh, Shawkat & Kim, Won Joong, 2015. "Forecasting the price of gold using dynamic model averaging," International Review of Financial Analysis, Elsevier, vol. 41(C), pages 257-266.
    2. Das, Debojyoti & Bhatia, Vaneet & Kumar, Surya Bhushan & Basu, Sankarshan, 2022. "Do precious metals hedge crude oil volatility jumps?," International Review of Financial Analysis, Elsevier, vol. 83(C).
    3. Tachibana, Minoru, 2022. "Safe haven assets for international stock markets: A regime-switching factor copula approach," Research in International Business and Finance, Elsevier, vol. 60(C).
    4. Evrim Mandacı, Pınar & Cagli, Efe Çaglar & Taşkın, Dilvin, 2020. "Dynamic connectedness and portfolio strategies: Energy and metal markets," Resources Policy, Elsevier, vol. 68(C).
    5. Baur, Dirk G. & Smales, Lee A., 2020. "Hedging geopolitical risk with precious metals," Journal of Banking & Finance, Elsevier, vol. 117(C).
    6. Michis, Antonis A., 2014. "Investing in gold: Individual asset risk in the long run," Finance Research Letters, Elsevier, vol. 11(4), pages 369-374.
    7. Liu, Zhenhua & Zhang, Huiying & Ding, Zhihua & Lv, Tao & Wang, Xu & Wang, Deqing, 2022. "When are the effects of economic policy uncertainty on oil–stock correlations larger? Evidence from a regime-switching analysis," Economic Modelling, Elsevier, vol. 114(C).
    8. Kang, Sanghoon & Hernandez, Jose Arreola & Sadorsky, Perry & McIver, Ronald, 2021. "Frequency spillovers, connectedness, and the hedging effectiveness of oil and gold for US sector ETFs," Energy Economics, Elsevier, vol. 99(C).
    9. Obryan Poyser, 2017. "Exploring the determinants of Bitcoin's price: an application of Bayesian Structural Time Series," Papers 1706.01437, arXiv.org.
    10. Lukáš Frýd, 2018. "Asymetrie během finančních krizí: asymetrická volatilita převyšuje důležitost asymetrické korelace [Asymmetry of Financial Time Series During the Financial Crisis: Asymmetric Volatility Outperforms," Politická ekonomie, Prague University of Economics and Business, vol. 2018(3), pages 302-329.
    11. Mohd Fahmi Ghazali & Hooi Hooi Lean & Zakaria Bahari, 2019. "Does Gold Investment Offer Protection Against Stock Market Losses? Evidence From Five Countries," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 65(02), pages 275-301, August.
    12. Pierdzioch, Christian & Risse, Marian & Rohloff, Sebastian, 2016. "Are precious metals a hedge against exchange-rate movements? An empirical exploration using bayesian additive regression trees," The North American Journal of Economics and Finance, Elsevier, vol. 38(C), pages 27-38.
    13. Yousaf, Imran & Beljid, Makram & Chaibi, Anis & Ajlouni, Ahmed AL, 2022. "Do volatility spillover and hedging among GCC stock markets and global factors vary from normal to turbulent periods? Evidence from the global financial crisis and Covid-19 pandemic crisis," Pacific-Basin Finance Journal, Elsevier, vol. 73(C).
    14. Abdelbari El Khamlichi & Thi Hong Van Hoang & Wing‐keung Wong, 2016. "Is Gold Different for Islamic and Conventional Portfolios? A Sectorial Analysis," Post-Print hal-02965765, HAL.
    15. Bonato, Matteo & Demirer, Riza & Gupta, Rangan & Pierdzioch, Christian, 2018. "Gold futures returns and realized moments: A forecasting experiment using a quantile-boosting approach," Resources Policy, Elsevier, vol. 57(C), pages 196-212.
    16. Bouoiyour, Jamal & Selmi, Refk & Wohar, Mark E., 2018. "Measuring the response of gold prices to uncertainty: An analysis beyond the mean," Economic Modelling, Elsevier, vol. 75(C), pages 105-116.
    17. Amélie Charles & Olivier Darné & Jae H. Kim, 2014. "Precious metals shine? A market efficiency perspective," Working Papers hal-01010516, HAL.
    18. Bedoui, Rihab & Guesmi, Khaled & Kalai, Saoussen & Porcher, Thomas, 2020. "Diamonds versus precious metals: What gleams most against USD exchange rates?," Finance Research Letters, Elsevier, vol. 34(C).
    19. Ghosh, Amit, 2016. "What drives gold demand in central bank's foreign exchange reserve portfolio?," Finance Research Letters, Elsevier, vol. 17(C), pages 146-150.
    20. Hoang, Thi-Hong-Van & Wong, Wing-Keung & Zhu, Zhenzhen, 2015. "Is gold different for risk-averse and risk-seeking investors? An empirical analysis of the Shanghai Gold Exchange," Economic Modelling, Elsevier, vol. 50(C), pages 200-211.

    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:gam:jmathe:v:8:y:2020:i:5:p:844-:d:361975. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.