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Licensed Unlicensed Requires Authentication Published by De Gruyter October 7, 2020

Time–Frequency Regression

Yoshito Funashima

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.

JEL classification: C49

Corresponding author: Yoshito Funashima, Faculty of Economics, Tohoku Gakuin University, 1-3-1 Tsuchitoi, Aoba-ku, Sendai, Miyagi 980-8511, Japan, E-mail: .

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.

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Published Online: 2020-10-07

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