Jump Test And Empirical Research Based On Behavior Path Of High Frequency Data

In recent years,with the vigorous development of the financial market,the financial return rate is the goal of chasing.The volatility of the financial return rate has become the most concerned issue for financial investment traders.Therefore,it is very important to study the volatility of stock market in financial market.In the actual stock market,there are many reasons for stock market fluctuations,such as macroeconomic fluctuations,changes in financial exchange rates,large fluctuations in interest rates,government policies and other factors,which will cause stock prices to change substantially in a very short period of time,that is,jump phenomenon.The existence of jump behavior will have a direct impact on the accuracy of volatility estimation and prediction of asset return,so the research of jump behavior in stock market volatility can not be ignored.It is a significant research problem to detect whether there is jump behavior in income fluctuation.Ait-Sahalia and Jacod use the realized variation theory to propose a test method for jumping behavior,called AJ test.This paper studies the following two problems on the AJ test of jumping behavior.(1)Under the condition of independent samples,whether the AJ test judges the jump behavior of asset prices under a limited sample is valid through simulated data.(2)Under the condition that the samples are dependent,whether the AJ test's judgment on asset price jump behavior under a limited sample is effective through simulated data.We know that the AJ test is obtained under the assumption of the standard diffusion process,and the model uses standard Brownian motion as the driving source.Since the increments of Brownian motion are independent of each other,this means that the sample series of logarithmic returns are independent of each other.But in reality these samples of logarithmic returns are often independent.So it needs to be analyzed:if the samples are dependent,whether the AJ test is still effective.In response to these two problems,we use the discrete asset price diffusion model of independent error or dependent error for numerical simulation,where the independent error is based on the standard Brownian motion model and the dependent error is the owner of the first-order autoregressive model.In the two cases with or without skipping behavior,study the asymptotic distribution of the statistics of AJ test The simulation study found that,whether it is an independent sample or a dependent sample,when the jump behavior is not included,the simulated distribution of the AJ test statistic is normal,and when the jump behavior is included,the simulated distribution of the AJ test statistic is not normal distributed.This means that whether it is an independent sample or a dependent sample,it is feasible to use the AJ test to judge the jump of the asset price process.Therefore,for independent or dependent discrete asset price models,the AJ test can make validity judgments on jumping behavior.Finally,based on the high-frequency data,this paper uses the realized volatility and the second variation to separate the jumping volatility.Model and analyze the continuity and jumping asset prices respectively.Using the sample training data and the actual Shanghai stock index,through the model comparison,observe the numerical characteristics of the jump test statistics,and confirm that there is a jump phenomenon in China's stock market.