The project focuses on studying multivariate time-frequency dynamics of financial markets using spectral methods. First target is to formulate new spectral-based realized measure of variance and covariance using wavelets, which will be applied to measure the integrated volatililty and covolatility under the various types of dependent microstructure noise. The newly proposed estimators will also allow studying behavior of the stock market participants at various scales representing investment horizons ranging from intraday up to several months. The second target is to utilize this new approach to propose methods for monitoring multi-scale systematic risk, which will allow measuring the risk varying not only in time but throuth frequencies as well. Our third target is to propose a wavelet test for co-jumps and study the impact of jumps and co-jumps on the density forecasts with direct implications to forecasting, risk management and portfolio allocation. Overall, the project hepls us to understand the dynamics of the financial markets from a new perspective.