A Wavelet-based Jump Information Criterion For High-frequency Financial Series Data

Detecting jumps in high-frequency financial series data and studying its dynamics is imperative in applications such as derivatives pricing and risk management.Although numerous methods to detect the presence of jumps have been introduced recently,they rely on the assumption that the number of jumps is known or multiple test procedure.Consequently,they are non-robust in the presence of jumps and could lead to spuri-ous detections in empirical studies.In addition,denoising high-frequency financial se-ries data with jumps is also significant because the denoising algorithm can clean the data and get the estimator of systematic pattern.Based on local linear scaling approx-imation(in short,LLSA)algorithm and the linear maximal overlap discrete wavelet transform(MODWT),we propose a wavelet-based jump information criterion(WJIC)in this paper for denoising and jump identification simultaneously and we optimally de-termine the parameters by using a score function.We conduct a simulation to compare the performance of WJIC and other methods and apply our algorithm with National As-sociation of Securities Dealers Automated Quotations(NASDAQ)Index.Asymptotic properties of the proposed estimators are derived and simulations and empirical studies demonstrate that the proposed estimator has good properties in terms of mean squared error.