Abstract
In this paper, we introduce a new time-domain decomposition for weakly stationary or trend stationary processes, based on trigonometric polynomial modeling of the underlying component of an economic time series. The method is explicitly devised to disentangle medium to long-term and short-term fluctuations in macroeconomic and financial series, to accurately measure the financial cycle and the concurrent long swings in economic activity. The implementation of this decomposition is straightforward and relies on standard regression analysis and general to specific model reduction. Full support to the proposed method is provided by Monte Carlo simulation. In the paper, we also provide a multivariate extension, involving sequential univariate decompositions and Principal Components Analysis. Based on this multivariate approach, we introduce a set of new composite indexes of macro-financial conditions for the euro area and assess their information content. In particular, concerning the current pandemic, the indicators suggest that most of the GDP contraction has been of short-term, cyclical nature. This is likely due to the prompt monetary and fiscal policy responses. Yet our evidence suggests that the financial cycle might have currently achieved a peak area. Hence, the risk of further, deeper disruptions is high, particularly in so far as a new sovereign/corporate debt crisis were not eventually avoided.
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