Research on MultiResolution Persistence and Common Persistence

To capture the changing relations of the financial risk with the time scale, a new definition of multiresolution persistence and common persistence is put forward based on the maximal overlap of discrete wavelet transform and the impulse response analysis. The former discussion about volatility persistence and common persistence has been expanded by the new definition. In the article, three states of the persistence are discussed, and the corresponding relations between common persistence and cointegration are demonstrated, which has important implications in optimal portfolio allocation decisions to reduce the impact of persistence on financial risk. Finally, an empirical example in Chinese stock market provides a simple illustration of the ideas.