A Nonlinear Filtering Algorithm based on Wavelet Transforms for High-Frequency Financial Data Analysis

The increased availability of high-frequency financial data has imposed new challenges for its denoising analysis since the data exhibits heavy tails and long-memory effects that render the application of traditional methods difficult. In this paper, we introduce the local linear scaling approximation (in short, LLSA), which is a nonlinear filtering algorithm based on the linear maximal overlap discrete wavelet transform (MODWT). We show the unique properties of LLSA and compare its performance with MODWT. We empirically show the superior performance of LLSA in smoothing analysis (i.e., trend extraction) of high- frequency data from German equity market. Based on our results we conclude that LLSA is reliable and suitable for high-frequency data denoising analysis.