Advanced topics in signal processing
A friendly guide to wavelets
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The joint time-frequency analysis (JTFA) is a signal processing technique in which signals are represented in both the time domain and the frequency domain simultaneously. Recently, this analysis technique has become an extremely powerful tool for analyzing nonstationary time series. One basic problem in business-cycle studies is how to deal with nonstationary time series. The market economy is an evolutionary system. Economic time series therefore contain stochastic components that are necessarily time dependent. Traditional methods of business cycle analysis, such as the correlation analysis and the spectral analysis, cannot capture such historical information because they do not take the time-varying characteristics of the business cycles into consideration. In this paper, we introduce and apply a new technique to the studies of the business cycle: the wavelet-based time-frequency analysis that has recently been developed in the field of signal processing. This new method allows us to characterize and understand not only the timing of shocks that trigger the business cycle, but also situations where the frequency of the business cycle shifts in time. Applying this new method to post war US data, we are able to show that 1973 marks a new era for the evolution of the business cycle since World War II.