Economic and financial time series are the result of the aggregation of phenomena operating at different frequencies. The presence of shocks with heterogeneous persistence is a relevant issue in the literature. The talk shows how to decompose weakly stationary time series into the sum, across time scales, of uncorrelated components associated with increasing degrees of persistence. It provides an Extended Wold Decomposition based on an isometric scaling operator that makes averages of process innovations. Thanks to the uncorrelatedness of such components, the obtained representation of a time series naturally induces a persistence-based variance decomposition of any weakly stationary process.  

The decomposition is applied to the determination of cycles in US stock market returns. The literature already acknowledges the presence of two- and six-week cycles associated with the occurrence of different kinds of Federal Reserve meetings. Such cycles can be exploited by a portfolio strategy that keeps only a share of the market index at alternate weeks (‘even-week strategy’). However, this investment rule misses a theoretical foundation. By the Extended Wold Decomposition, we provide a rigorous framework for the detection of stock market cycles and the determination of optimal portfolio choices that profit from such periodicities, outperforming the even-week strategy. 

Main reference 

Ortu, Severino, Tamoni, Tebaldi (2020) A persistence-based Wold-type decomposition for stationary time series. Quantitative Economics, 11(1), 203-230.