Estimation And Application Study On Covariance Matrix Of High Frequency Data Based On Market Microstructure Noises And Jumps

The covariance matrix of the financial assets plays an important role in the portfolio and risk management. There is a big difference in Covariance matrix if they are calculated by different methods, the mainstream calculation method is still based on low frequency data, but the low frequency data lost a lot of useful information, so that the covariance matrix of the estimated less than ideal. In order to improve the accuracy of the estimate of the covariance matrix, it is necessary to study the covariance matrix based on the high-frequency data, high frequency data contains more useful information than the low-frequency data, and contains information will increase with the increase of sampling frequency.Common covariance matrix estimation model based on the low-frequency data can not meet the requirement of the covariance matrix modeling of high-frequency data, it is necessary to propose a new method to estimate the covariance matrix of the high-frequency data. Andersen and Bollerslev (2003) proposed the realized covariance matrix RCOV, it is the most commonly used method to estimate the covariance matrix of the high frequency data, realized covariance matrix does not require complex parameter estimation and does not need to create a model, it is relatively simple to calculate and can be application in financial risk management, so the covariance matrix has been widely used.However, with the increase of the sampling frequency, high-frequency data contained more and more rich information, but at the same time, the impact of market microstructure noises will be more obvious. Moreover, return on assets will undergo substantial fluctuations in short span of time under certain circumstances, resulting in jumping; jumps will also cause no ignorable influence on the estimation of high-frequency data covariance matrix. In recent years, with the in-depth study of the high-frequency covariance matrix, many scholars have begun to consider the impact of the market microstructure noise or jump on the high-frequency covariance matrix estimation, they pointed out that when the market microstructure noise or jumps exist, realized covariance matrix is no longer a consistent estimator to the integral covariance matrix, so they proposed new covariance matrix estimator to reduce market microstructure noise or jumps affect. However, most of the existing literatures have only studied how to reduce the impact of the market microstructure noises on the estimation of high frequency covariance matrix, or only considered how to eliminate jump effects on high frequency data. There is little literature taking into account the impact of the noise and jumping on the estimation of high frequency covariance matrix simultaneously. Both the microstructure noises and jumps may exit simultaneously in the financial market. Under such conditions, it is still a difficult task to estimate the covariance matrix of high frequency data, there is little literature to study it.When the microstructure noises and jumps exist simultaneously, this dissertation proposes a new estimator—Modified Threshold Pre-averaging Realized Covariance Matrix (MTPCOV), this estimator can reduce the impact of microstructure noises by pre-averaging method, and can exclude the impact of jumps. This paper first discusses the theoretical properties of the MTPCOV estimator, and then carries out empirical test on the estimator by means of simulation data and real stock high-frequency data. When we estimate the high-frequency covariance matrix MTPCOV, in order to solve the different trading problems, we often using the refresh time program of high-frequency data synchronization process, the amount of the data loss will be very large, especially when we consider the large number of assets. In order to reduce the loss of data and get more accurate high-frequency covariance matrix estimator, this article will apply blocking strategy and regularization method to the estimation of MTPCOV, and get the Blocking and Regularization Modified Threshold Pre-averaging Realized Covariance Matrix which based on the liquidity adjustment, In addition, the this dissertation also compare the commonly used high-frequency covariance matrix forecasting model to select the best forecasting model, and further study the application of MTPCOV estimator and the RnBMTPCOV estimator in portfolio. This dissertation combines closely the theory of volatility of high-frequency data, analysis methods in financial econometrics, and empirical research and also combines the qualitative and quantitative methods. It has not only the theory research and construction but also the detailed empirical analysis. The specific content of this dissertation is as follows:The first chapter is an introduction section. This chapter introduces the research background, pointed out that the purpose and significance of the study, and given the main research content of this dissertation and the main innovations.The second chapter is a review of the literature of this dissertation. This chapter first reviews the theory of one-dimensional high-frequency fluctuations in the data, and then carries out a detailed introduction to the estimation method of the realized covariance matrix, further reviews the current research of the covariance matrix estimator of high-frequency data under the condition of market microstructure noises and jumps respectively, finally, inductive analysis of the domestic and foreign literature about the applications of the high-frequency data in portfolio.The third chapter proposes a new estimator—Modified Threshold Pre-averaging Realized Covariance Matrix, which is based on the market microstructure noises and jumps. This chapter first introduces the improved pre-averaging method, which can eliminate the impact of market microstructure noises on estimation of covariance matrix of high-frequency data, and recalls the estimation method of high-frequency covariance matrix which is based on the improved pre-averaging method. Although Pre-averaging Realized Covariance Matrix estimator can eliminate the effects of market microstructure noises, it cannot handle the effects of jumps on the estimation. Then how to estimate the covariance matrix of high-frequency data under the existence of both market microstructures noises and jumps? To this end, this chapter proposes a new estimator-Modified Threshold Pre-averaging Realized Covariance Matrix, this estimator combines the pre-averaging method and the threshold thinking method and it can eliminate the impact of market microstructure noises and jumps simultaneously. The main diagonal elements of the MTPCOV are Modified Threshold Pre-averaging Realized Volatility (MTPRV). The sub-diagonal elements of the MTPCOV estimator are Modified Threshold Pre-averaging Realized Covariance. Ma Dan, Yin You ping (2012) proves the ultimate nature of MTPRV, and points out that it is the consistent estimator of the integral volatility, and proves MTPRV estimator is better than other volatility estimators of high-frequency data through simulation studies. This chapter mainly discusses the limit properties of the MTPCV estimator, and proves it is a consistent estimator of the integral covariance, and the simulate it. According to the convergence properties of the matrix, we know that the MTPCOV estimator which is constructed by MTPRV and MTPCV is the consistent estimator of the integral covariance matrix.The fourth chapter applies blocking strategy and regularization method to the estimation of Modified Threshold Pre-averaging Realized Covariance Matrix, thus reducing the loss of data, and gets the positive definite and more accurate covariance matrix estimator—Modified Threshold Pre-averaging Realized Covariance Matrix which is based on the liquidity adjustment. This chapter first introduces the refresh time program, and then analyzes the loss of data of the MTPCOV which is based on the refresh time program. Introduces the blocking strategy and regularization method, and applies them to the estimation of the MTPCOV estimator, thus gets the RnBMTPCOV estimator. Finally, researches on the effectiveness of the RnBMTPCOV, and compares the RnBMTPCOV estimator with MTPCOV estimator, gets the conclusion that the RnBMTPCOV estimator is more accurate covariance matrix.The fifth chapter first describes the covariance matrix forecasting model based on high-frequency data as well as the typical covariance matrix forecasting model based on the low-frequency data, and then detailed introduce the MCS test which is the comparison method of the foresting models. Through the study, we find that the LOG-HAR model which is based on the logarithmic transformation of the matrix is the best forecasting model, it has the best performance in all of the loss function, The LOG-HAR model ensures the positive definiteness of the predicted covariance matrix on the one hand, and captures the long memory of the time series on the other hand. Therefore, in the later study, we will use the LOG-HAR model to predict the covariance matrix of the high-frequency data.The sixth chapter is the empirical analysis of the high-frequency covariance matrix applications in the portfolio. The first part of this chapter introduces the application of high-frequency covariance matrix in portfolio, and analysis of the problem of portfolio optimization. Section II introduces the empirical analysis methods, the volatility timing strategies and the comparison methods of several dynamic portfolios. Section III of this chapter is the empirical part; this section first introduces the selection and processing of the data, and then carries out a detailed analysis of the empirical results.The seventh chapter is the conclusion and outlook of this dissertation. Research work of this dissertation is summarized in this chapter and future research directions and fields are pointed out.Innovation of this dissertation can be summarized as follows:(1) A new covariance matrix of high-frequency data is proposed, namely Modified’Threshold Pre-averaging Realized Covariance Matrix (MTPCOV)When the financial markets meet the assumption of the efficient markets, that there are no market noises or jumps, the realized covariance matrix (RCOV) is the consistent estimator of the integral covariance matrix.But on the reality of financial markets, existing microstructure noises and jumps, and the impact of the noises or jumps can’t be ignored, so that the realized covariance matrix is no longer the consistent estimator of the integral covariance matrix. To solve this problem, many scholars have put forward a variety of methods to deal with noises or jumps to estimate the covariance matrix of high frequency data accurately. However, most of the existing literatures have only studied how to reduce the impact of the market microstructure noises on the estimation of high frequency covariance matrix, or only considered how to eliminate jump effects on high frequency data. There is little literature taking into account the impact of the noise and jumping on the estimation of high frequency covariance matrix simultaneously. Both the microstructure noises and jumps may exit simultaneously in the financial market. Under such conditions, it is still a difficult task to estimate the covariance matrix of high frequency data, there is little literature to study it. This paper applies the threshold to the Modulated realized covariance Matrix which is based on the pre-averaging method to exclude the effects of jumps. And proposes a new estimator—Modified Threshold Pre-averaging Realized Covariance Matrix (MTPCOV), it can eliminate the impact of market microstructure noises and jumps simultaneously. In addition, this paper also discusses the statistical properties of the MTPCOV estimator, and proves it is the consistent estimator of the integral covariance matrix, and the estimator has the optimal convergence rate.(2)This dissertation applies blocking strategy and regulation method in the estimation of MTPCOV to reduce the amount of data loss, and gets the RnBMTPCOV estimator which is based on the liquidity adjustment.When we estimate the high-frequency covariance matrix MTPCOV, in order to solve the different trading problems, we often using the refresh time program of high-frequency data synchronization process, which will make the data loss is very large, especially when we consider the large number of assets. In order to reduce the loss of data and get more accurate high-frequency covariance matrix estimator, this article will apply blocking strategy and regularization method to the estimation of MTPCOV, and get the Blocking and Regularization Modified Threshold Pre-averaging Realized Covariance Matrix which based on the liquidity adjustment. This estimator is the adjustment of the Modified Threshold Pre-averaging Realized Covariance Matrix, overcomes its shortcomings resulted in substantial loss of data due to the refresh time sampling, without imposing any restrictions to the parameters to improve the estimation accuracy.(3) This dissertation applies the covariance matrix of high frequency data which is proposed by this dissertation to the portfolio, and compares it with other methods.The studies of high-frequency data are concentrated in the one-dimensional in domestic, and the studies of the multi-dimensional covariance matrix of high frequency data are very little. Individual literature related to the covariance matrix of the high-frequency data, but there are no studies of the application of the MTPCOV in portfolio or the estimation of the MTPCOV which can eliminate the microstructure noises and jumps in domestic. This dissertation applies the MTPCOV and the RnBMTPCOV to the portfolio, and compares it with other covariance matrix of high frequency data methods by variety of standard, systematic and comprehensive analysis of high-frequency covariance matrix estimation method and its application in the portfolio.