Wavelet decomposition of the financial cycle: An early warning system for financial tsunamis

We propose a wavelet-based approach for construction of a financial cycle proxy. Specifically, we decompose three key macro-financial variables – private credit, house prices, and stock prices – on a frequency-scale basis using wavelet multiresolution analysis. The resulting "wavelet-based" sub-series are aggregated into a composite index representing our cycle proxy. Selection of the sub-series deemed most relevant is done by emphasizing early warning properties. The wavelet-based financial cycle proxy is shown to perform well in detecting banking crises in out-of-sample exercises, outperforming the credit-to-GDP gap and a financial cycle proxy derived using the approach of Schüler et al. (2015).