Over the past few years, we have seen an increased need for analyzing the dynamically changing behaviors of economic and financial time series. These needs have led to significant demand for methods that denoise non-stationary time series across time and for specific investment horizons (scales) and localized windows (blocks) of time. This thesis consists of a three-part series of papers. The first paper develops a wavelet framework for the finance and economics community to quantify dynamic, interconnected relationships between non-stationary time series. The second paper introduces a novel continuous wavelet transform, dynamically-optimized, multivariate thresholding method to extract the optimal signal from multivariate time series. Finally, the third paper presents an augmented stochastic volatility wavelet-based forecasting method building on the partial mixture distribution modeling framework introduced in the second paper. Promising results in economics and finance have come from implementing wavelet analysis, however more advanced wavelet techniques are needed as well as more robust statistical analysis tools. In support of this expansion effort, we developed a comprehensive and user-friendly R package, CoFESWave, containing our newly developed thresholding and forecasting methods.