| Due to the unobservability of volatility,the estimation of volatility has always been an important issue of concern in financial markets.Volatility models play a significant role in modeling and forecasting the volatility,correlations,and risk indicators of various financial assets.With the rapid development of computer technology,data storage capacity has been enhanced,and the channels and methods for obtaining high-frequency data have become more convenient.In comparison to daily frequency data,intraday highfrequency return series contain more useful information,which can improve the accuracy of volatility estimation.Taking the above into consideration,this thesis introduces intraday high-frequency data into nonparametric and semiparametric volatility models,aiming to enhance the precision of volatility estimation by integrating information from intraday high-frequency data.Firstly,this thesis proposes a class of nonparametric volatility proxy models and explores the estimation of nonparametric GARCH model volatility using intraday highfrequency data.Traditional nonparametric GARCH models define an unknown bivariate function to express volatility and obtain volatility estimates through a convergent iterative algorithm.In comparison to standard parametric GARCH models,particularly in cases of asymmetry and other deviations from the standard GARCH specification,the advantages of the nonparametric GARCH model’s fit are more apparent.Building upon this,we use realized volatility as a proxy variable and establish a class of nonparametric volatility proxy models.Under certain assumptions,we derive the asymptotic bias and variance of the estimators and discuss the impact of volatility proxies at different frequencies on estimation accuracy.Based on simulation and empirical studies,our conclusion is that the precision of the volatility function estimation in the nonparametric GARCH model can be significantly improved by incorporating intraday high-frequency data information.Secondly,this thesis proposes a class of semiparametric volatility proxy models and examines the parameter and volatility estimation issues of the semiparametric GARCH model based on intraday high-frequency data.Traditional semiparametric models define a non-negative smooth-link function to express volatility,constraining excessive growth in volatility to fit the volatility dynamics.In comparison to parametric GARCH models,this model demonstrates clear advantages in modeling volatilities with geometric decay rates and leverage effects.Building upon this,we propose a class of semiparametric volatility proxy models using realized volatility as a proxy variable.Under certain assumptions,we establish the asymptotic normality of the function and parameter estimators.Furthermore,we investigate the impact of volatility proxies at different frequencies on the estimation precision of the volatility function and its parameters.Simulation and empirical studies indicate that incorporating intraday high-frequency data information into the daily-frequency semiparametric GARCH model effectively enhances the estimation precision of the model’s volatility function and parameters.Furthermore,this thesis proposes a class of additive volatility proxy models and investigates the estimation problem of the volatility function in the intraday proportional additive model based on high-frequency data.The component functions of traditional additive models can be estimated can be estimated using methods such as back-fitting and marginal integration for obtaining univariate convergence rates.When the components are proportional,a direct local polynomial estimator can be employed.Building on this,the thesis considers a feasible approach to incorporating high-frequency data into the direct local polynomial estimator.Under mild conditions,the asymptotic normality of estimators is established.Furthermore,simulation and empirical results demonstrate that the introduction of high-frequency data significantly enhances the estimation accuracy of the volatility function compared to estimates obtained using daily frequency data.Finally,based on actual data,this thesis discusses the criteria for selecting volatility proxies and the optimal sampling frequency for the intraday nonparametric ARCH(1)model.According to existing research,the estimation accuracy of high-frequency(G)ARCH models is largely dependent on the sampling frequency of the data used.Considering this,within a nonparametric framework,this thesis empirically investigates the influence of sampling frequency on the estimation accuracy of(G)ARCH models.For simplicity,focusing on the intraday nonparametric ARCH(1)model,we propose a criterion for selecting the optimal volatility proxy based on the asymptotic properties of the model,and discuss the optimal sampling frequency for different types of volatility proxies.Through empirical analysis of high-frequency intraday data of the Shanghai Stock Exchange Composite Index(000001),the results reveal significant differences in the estimation performance of volatility proxies at different sampling frequencies.Additionally,even at the same sampling frequency,different volatility proxies demonstrate distinct estimation effects.Therefore,when conducting research on the estimation of nonparametric and semiparametric volatility models using high-frequency intraday data,careful selection of the optimal volatility proxies and their sampling frequencies is crucial as it significantly impacts the accuracy of volatility estimation.In summary,the objective of this thesis is to incorporate intraday high-frequency data into several categories of daily nonparametric and semiparametric volatility models,and to utilize high-frequency data information to construct corresponding volatility proxy models,aiming to enhance the accuracy of volatility estimation in these models.This research carries significant theoretical and practical implications. |
