A multiscale estimator for pricing error decomposition in high-frequency financial markets

For a L & eacute;vy process corrupted with microstructure noise, sampling distributions are derived for the information-related and information-unrelated pricing error parameters and for the variance of latent true price returns (a noise-robust and consistent estimator of realized variance). The test statistics converge in distribution to the standard normal distribution, while statistics for joint tests, tests for intraday seasonality, and tests for time varying parameters converge in distribution to the chi 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\chi }<^>{2}$$\end{document} distribution. Simulation evidence verifies that test statistics display good size and power properties. As an application, the proposed tests are taken to a sample of exchange rates, commodities, and index futures.