Detecting global financial crises with scarce data by multivariate nonlinear filtering

Abstract An original procedure is devised for the automated detection of global financial crises from multivariate databases of share prices. It consists of: i) the construction of time series from the time-windowed estimations of crisis relevant information (cross-correlations or volatilities); ii) the piecewise-linear filtering of times series by nonlinear filtering, achieved by nonsmooth proximal minimization implemented by an efficient iterative algorithm; iii) the estimation of a reassigned time in each window; iv) the detection of crises and estimation of their intensities by exploiting the multivariate structure of denoised time series. Applied to a world dataset of 32 indices over 6 decades, this original model based procedure detects all major crises from the reference lists. It also permits to devise a typology in reference to an archetypal financial crisis. It is automated, data-driven and reproducible notably for the analysis of financial crises over history, or contemporary crises on worldwide databases, via a novel toolbox. Finally it is robust to scarce, incomplete and noisy data.