A new wavelet‐based denoising algorithm for high‐frequency financial data mining

Denoising analysis imposes new challenge for mining high‐frequency financial data due to its irregularities and roughness. Inefficient decomposition of the systematic pattern (the trend) and noises of high‐frequency data will lead to erroneous conclusion as the irregularities and roughness of the data make the application of traditional methods difficult. In this paper, we propose the local linear scaling approximation (in short, LLSA) algorithm, a new nonlinear filtering algorithm based on the linear maximal overlap discrete wavelet transform (MODWT) to decompose the systematic pattern and noises. We show several unique properties of this brand‐new algorithm, that are, the local linearity, computational complexity, and consistency. We conduct a simulation study to confirm these properties we have analytically shown and compare the performance of LLSA with MODWT. We then apply our new algorithm with the real high‐frequency data from German equity market to investigate its implementation in forecasting. We show the superior performance of LLSA and conclude that it can be applied with flexible settings and suitable for high‐frequency data mining.