A Continuous Differentiable Wavelet Shrinkage Function for Economic Data Denoising

In economic (financial) time series analysis, prediction plays an important role and the inclusion of noise in the time series data is also a common phenomenon. In particular, stock market data are highly random and non-stationary, thus they contain much noise. Prediction of the noise-free data is quite difficult when noise is present. Therefore, removal of such noise before predicting can significantly improve the prediction accuracy of economic models. Based on this consideration, this paper proposes a new shrinkage (thresholding) function to improve the performance of wavelet shrinkage denoising. The proposed thresholding function is an arctangent function with several parameters to be determined and the optimal parameters are determined by ensuring that the thresholding function satisfies the condition of continuously differentiable. The closing price data with the Shanghai Composite Index from January 1991 to December 2014 are used to illustrate the application of the proposed shrinkage function in denoising the stock data. The experimental results show that compared with the classical shrinkage (hard, soft, and nonnegative garrote) functions, the proposed thresholding function not only has the advantage of continuous derivative, but also has a very competitive denoising performance.