Lt(?) Semimartingale Testing Under Microstructure Noise

When we use high-frequency financial data to study the asset price process in the financial market,we will inevitably encounter the problem of microstructure noise.The impact of microstructure noise in the financial market can not be ignored.If we directly use high-frequency financial data polluted by microstructure noise to estimate the problem in asset pricing modeling,it may make the model estimation inaccurate.Therefore,in order to accurately estimate and infer the model,we must first reduce the impact of microstructure noise.At present,many scholars have proposed noise reduction methods.At the same time,we know that the semimartingale process is widely used in the research of financial high-frequency data.It is a process that can represent the price change of non-arbitrage assets.In the semimartingale,It(?) semimartingale is a more special kind of semimartingale.When we use the semimartingale to describe the asset price process,we usually use It(?) semimartingale,but there are also some problems in the application,that is,when the asset price process is not It(?) semimartingale,Using the It(?) semimartingale framework to study may lead to the problem that the error of the parameter estimator in the model becomes larger and the estimation is inaccurate.For this problem,some scholars have proposed the It(?) semimartingale hypothesis test method to determine whether the price process is It(?) semimartingale.This paper will first use the pre-averaging threshold method to reduce the impact of microstructure noise,improve the test statistics in It(?)’s semimartingale hypothesis test,construct a new test statistic,and then verify through numerical simulation that the pre-averaging threshold method is better than the quadratic variation method in reducing microstructure noise,and indirectly obtain the asymptotic normality of the new statistics,Finally,this paper selects the price data of some domestic focused stock indexes and constituent stocks for empirical analysis,compares the hypothesis test results of It(?) semimartingale under different sample sizes and different sampling periods,and draws some important conclusions,which provides important practical guidance for the subsequent research of It(?) semimartingale hypothesis test.