The project focuses on analysis of financial time series in a framework of bivariate long memory with a special attention on power-law decaying cross-correlation function and its implications for dynamic properties of such processes. The first target is to use these implications for construction of statistical tests to distinguish between short and long memory. The second aim is to explore the possibility of processes having the power-law form of squared spectrum coherency by introducing several tests and estimators of the power-law coherency parameter together with their finite sample properties. The third target is to investigate the estimators of the bivariate long memory parameters and introduce new spectrum-based estimators. Overall, the project aims to propose a way how to treat long-range cross-correlated processes in finance environment starting from testing for the presence of memory, then checking the power-law coherency and in turn estimating the bivariate memory parameter with a focus on standard financial stylized facts.