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.
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 17K03770, 18K01696
Acknowledgments
The author is extremely grateful to an anonymous referee and Raffaella Giacomini (the Editor) for very important comments that greatly improved this paper. The author also thanks Takeo Hori, Daichi Shirai, Kouki Sugawara, and Kizuku Takao for their helpful comments early on in the course of this study. This work was supported by Grants-in-Aid for Scientific Research by the Japan Society for the Promotion of Science (No. 17K03770, 18K01696). The usual disclaimer applies.
References
Aguiar-Conraria, L., and M. J. Soares. 2011a. “Business Cycle Synchronization and the Euro: A Wavelet Analysis.” Journal of Macroeconomics 33: 477–89. https://doi.org/10.1016/j.jmacro.2011.02.005.Search in Google Scholar
Aguiar-Conraria, L., and M. J. Soares. 2011b. “Oil and the Macroeconomy: Using Wavelets to Analyze Old Issues.” Empirical Economics 40: 645–55. https://doi.org/10.1007/s00181-010-0371-x.Search in Google Scholar
Aguiar-Conraria, L., and M. J. Soares. 2014. “The Continuous Wavelet Transform: Moving beyond Uni-And Bivariate Analysis.” Journal of Economic Surveys 28: 344–75. https://doi.org/10.1111/joes.12012.Search in Google Scholar
Aguiar-Conraria, L., M. M. F. Martins, and M. J. Soares. 2012. “The Yield Curve and the Macro-Economy across Time and Frequencies.” Journal of Economic Dynamics and Control 36: 1950–70. https://doi.org/10.1016/j.jedc.2012.05.008.Search in Google Scholar
Aguiar-Conraria, L., M. M. F. Martins, and M. J. Soares. 2018. “Estimating the Taylor Rule in the Time–Frequency Domain.” Journal of Macroeconomics 57: 122–37. https://doi.org/10.1016/j.jmacro.2018.05.008.Search in Google Scholar
Aguiar-Conraria, L., M. M. F. Martins, and M. J. Soares. 2020. “Okun’s Law across Time and Frequencies.” Journal of Economic Dynamics and Control 116: 103897. https://doi.org/10.1016/j.jedc.2020.103897.Search in Google Scholar
Ahmed, S., A. Levin, and B. A. Wilson. 2004. “Recent U.S. Macroeconomic Stability: Good Policies, Good Practices, or Good Luck?.” The Review of Economics and Statistics 86: 824–32. https://doi.org/10.1162/0034653041811662.Search in Google Scholar
Boivin, J., and M. Giannoni. 2006. “Has Monetary Policy Become More Effective?.” The Review of Economics and Statistics 88: 445–62. https://doi.org/10.1162/rest.88.3.445.Search in Google Scholar
Clarida, R., J. Galí, and M. Gertler. 2000. “Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory.” Quarterly Journal of Economics 115: 147–80. https://doi.org/10.1162/003355300554692.Search in Google Scholar
Crowley, P. M., and D. Hudgins. 2015. “Fiscal Policy Tracking Design in the Timefrequency Domain Using Wavelet Analysis.” Economic Modelling 51: 502–14. https://doi.org/10.1016/j.econmod.2015.09.001.Search in Google Scholar
Dima, B., Ş. M. Dima, and F. Barna. 2015. “A Wavelet Analysis of Capital Markets’ Integration in Latin America.” Applied Economics 47: 1019–36. https://doi.org/10.1080/00036846.2014.987917.Search in Google Scholar
Funashima, Y. 2017. “Time-varying Leads and Lags across Frequencies Using a Continuous Wavelet Transform Approach.” Economic Modelling 60: 24–8. https://doi.org/10.1016/j.econmod.2016.08.024.Search in Google Scholar
Funashima, Y. 2020. “Money Stock Versus Monetary Base in Time–Frequency Exchange Rate Determination.” Journal of International Money and Finance 104: 102150. https://doi.org/10.1016/j.jimonfin.2020.102150.Search in Google Scholar
Gallegati, M., M. Gallegati, J. B. Ramsey, and W. Semmler. 2011. “The US Wage Phillips Curve Across Frequencies and Over Time.” Oxford Bulletin of Economics & Statistics 73(4): 489–508. https://doi.org/10.1111/j.1468-0084.2010.00624.x.Search in Google Scholar
Ko, J. H., and Y. Funashima. 2019. “On the Sources of the Feldstein–Horioka Puzzle Across Time And Frequencies.” Oxford Bulletin of Economics & Statistics 81(4): 889–910. https://doi.org/10.1111/obes.12293.Search in Google Scholar
Ko, J. H., and C. M. Lee. 2015. “International Economic Policy Uncertainty and Stock Prices: Wavelet Approach.” Economics Letters 134: 118–22. https://doi.org/10.1016/j.econlet.2015.07.012.Search in Google Scholar
Kurowski, Ł., and K. Rogowicz. 2018. “Are Business and Credit Cycles Synchronised Internally or Externally?.” Economic Modelling 74: 124–41. https://doi.org/10.1016/j.econmod.2018.05.009.Search in Google Scholar
Mandler, M., and M. Scharnagl. 2014. Money Growth and Consumer Price Inflation in the Euro Area: A Wavelet Analysis. Deutsche Bundesbank: Discussion Paper. No. 33/2014.10.2139/ssrn.2797012Search in Google Scholar
Primiceri, G. E. 2005. “Time Varying Structural Vector Autoregressions and Monetary Policy.” The Review of Economic Studies 72: 821–52. https://doi.org/10.1111/j.1467-937x.2005.00353.x.Search in Google Scholar
Reboredo, J. C., and M. A. Rivera-Castro. 2014. “Wavelet-based Evidence of the Impact of Oil Prices on Stock Returns.” International Review of Economics & Finance 29: 145–76. https://doi.org/10.1016/j.iref.2013.05.014.Search in Google Scholar
Rua, A. 2010. “Measuring Comovement in the Time–Frequency Space.” Journal of Macroeconomics 32: 685–91. https://doi.org/10.1016/j.jmacro.2009.12.005.Search in Google Scholar
Rua, A. 2012. “Money Growth and Inflation in the Euro Area: A Time-Frequency View.” Oxford Bulletin of Economics & Statistics 74: 875–85. https://doi.org/10.1111/j.1468-0084.2011.00680.x.Search in Google Scholar
Rua, A. 2013. “Worldwide Synchronization Since the Nineteenth Century: A Wavelet Based View.” Applied Economics Letters 20: 773–6. https://doi.org/10.1080/13504851.2012.744129.Search in Google Scholar
Rua, A., and L. C. Nunes. 2012. “A Wavelet-Based Assessment of Market Risk: The Emerging Markets Case.” The Quarterly Review of Economics and Finance 52: 84–92. https://doi.org/10.1016/j.qref.2011.12.001.Search in Google Scholar
Tiwari, A. K. 2013. “Oil Prices and the Macroeconomy Reconsideration for Germany: Using Continuous Wavelet.” Economic Modelling 30: 636–42. https://doi.org/10.1016/j.econmod.2012.11.003.Search in Google Scholar
Verona, F. 2016. “Time–frequency Characterization of the U.S. Financial Cycle.” Economics Letters 144: 75–9. https://doi.org/10.1016/j.econlet.2016.04.024.Search in Google Scholar
Verona, F. 2020. “Investment, Tobin’s Q, and Cash Flow Across Time and Frequencies.” Oxford Bulletin of Economics & Statistics 82: 331–46. https://doi.org/10.1111/obes.12321.Search in Google Scholar
Yang, L., and S. Hamori. 2015. “Interdependence between the Bond Markets of CEEC-3 and Germany: A Wavelet Coherence Analysis.” The North American Journal of Economics and Finance 32: 124–38. https://doi.org/10.1016/j.najef.2015.02.003.Search in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston
