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Time–Frequency Regression

Author

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  • Funashima Yoshito

    (Faculty of Economics, Tohoku Gakuin University, 1-3-1 Tsuchitoi, Aoba-ku, Sendai, Miyagi 980-8511, Japan)

Abstract

Wavelet analysis is widely used to trace macroeconomic and financial phenomena in time–frequency domains. However, existing wavelet measures diverge from conventional regression estimators. Furthermore, a direct comparison between wavelet and traditional regression analyses is difficult. In this study, we modify the partial wavelet gain to provide an estimator that corresponds to the ordinary least squares estimator at each point of the time–frequency space. We argue that from the viewpoint of practical applications, the modified partial wavelet gain is suitable for contemporary regressions across time and frequencies, whereas the original partial wavelet gain is suitable for evaluating an aggregate relationship of contemporaneous and lead-lag relationships.

Suggested Citation

  • Funashima Yoshito, 2021. "Time–Frequency Regression," Journal of Econometric Methods, De Gruyter, vol. 10(1), pages 21-32, January.
    • Handle: RePEc:bpj:jecome:v:10:y:2021:i:1:p:21-32:n:1
    DOI: 10.1515/jem-2019-0025
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    References listed on IDEAS

    as
    1. Funashima, Yoshito, 2020. "Money stock versus monetary base in time–frequency exchange rate determination," Journal of International Money and Finance, Elsevier, vol. 104(C).
    2. Jun‐Hyung Ko & Yoshito Funashima, 2019. "On the Sources of the Feldstein–Horioka Puzzle across Time and Frequencies," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(4), pages 889-910, August.
    3. Mandler, Martin & Scharnagl, Michael, 2014. "Money growth and consumer price inflation in the euro area: A wavelet analysis," Discussion Papers 33/2014, Deutsche Bundesbank.
    4. 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.
    5. Richard Clarida & Jordi Galí & Mark Gertler, 2000. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(1), pages 147-180.
    6. Luís Aguiar-Conraria & Maria Soares, 2011. "Oil and the macroeconomy: using wavelets to analyze old issues," Empirical Economics, Springer, vol. 40(3), pages 645-655, May.
    7. António Rua, 2012. "Money Growth and Inflation in the Euro Area: A Time-Frequency View," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(6), pages 875-885, December.
    8. 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.
    9. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 821-852.
    10. Yang, Lu & Hamori, Shigeyuki, 2015. "Interdependence between the bond markets of CEEC-3 and Germany: A wavelet coherence analysis," The North American Journal of Economics and Finance, Elsevier, vol. 32(C), pages 124-138.
    11. Ko, Jun-Hyung & Lee, Chang-Min, 2015. "International economic policy uncertainty and stock prices: Wavelet approach," Economics Letters, Elsevier, vol. 134(C), pages 118-122.
    12. Funashima, Yoshito, 2017. "Time-varying leads and lags across frequencies using a continuous wavelet transform approach," Economic Modelling, Elsevier, vol. 60(C), pages 24-28.
    13. 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.
    14. Tiwari, Aviral Kumar, 2013. "Oil prices and the macroeconomy reconsideration for Germany: Using continuous wavelet," Economic Modelling, Elsevier, vol. 30(C), pages 636-642.
    15. Crowley, Patrick M. & Hudgins, David, 2015. "Fiscal policy tracking design in the time–frequency domain using wavelet analysis," Economic Modelling, Elsevier, vol. 51(C), pages 502-514.
    16. Luís Aguiar-Conraria & Maria Joana Soares, 2014. "The Continuous Wavelet Transform: Moving Beyond Uni- And Bivariate Analysis," Journal of Economic Surveys, Wiley Blackwell, vol. 28(2), pages 344-375, April.
    17. Reboredo, Juan C. & Rivera-Castro, Miguel A., 2014. "Wavelet-based evidence of the impact of oil prices on stock returns," International Review of Economics & Finance, Elsevier, vol. 29(C), pages 145-176.
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    More about this item

    Keywords

    ordinary least squares; time–frequency regression; wavelet gain;
    All these keywords.

    JEL classification:

    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other

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