Analysis of non-stationary dynamics in the financial system

Novel data-driven analyses, appropriate for detecting economic instability in non-stationary time series, are developed using functional principal component analysis (fPCA) and Synchrosqueezing. fPCA is applied in a new way, aggregating multiple financial time series to identify periods of macroeconomic instability. Synchrosqueezing, a technique which generates a time-series' time-dependent spectral decomposition, is modified to develop a new quantitative measure of local dynamical changes and structural breaks. The merit of this integrated technique is demonstrated by analyzing financial data from 1986 to 2012 that includes equity indices, securities and commodities, and foreign exchange. Both procedures successfully detect key historic periods of instability. Moreover, the results reveal distinctions between periods of long-term gradual change in addition to structural breaks. These tools offer new insights into the analysis of financial instability.