Generalized optimal wavelet decomposing algorithm for big financial data

Using big financial data for the price dynamics of U.S. equities, we investigate the impact that market microstructure noise has on modeling volatility of the returns. Based on wavelet transforms (DWT and MODWT) for decomposing the systematic pattern and noise, we propose a new wavelet-based methodology (named GOWDA, i.e., the generalized optimal wavelet decomposition algorithm) that allows us to deconstruct price series into the true efficient price and microstructure noise, particularly for the noise that induces the phase transition behaviors. This approach optimally determines the wavelet function, level of decomposition, and threshold rule by using a multivariate score function that minimizes the overall approximation error in data reconstruction. The data decomposition method enables us to estimate and forecast the volatility in a more efficient way than the traditional methods proposed in the literature. Through the proposed method we illustrate our simulation and empirical results of improving the estimation and forecasting performance.