Time–Frequency Regression

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.