Research On Intraday Volatility Of CSI 300 Index Based On Functional Data

Volatility plays a vital role in asset pricing,asset portfolio,risk management,etc.,so Markowitz(1952)has been the focus of research in the financial market since it first proposed the concept of volatility.It is also because of the concept of volatility that financial has officially developed into a new independent discipline.Therefore,the status and importance of volatility in the financial field is self-evident.According to the theory of financial volatility,the actual volatility is a function of time,and time is continuous,so the volatility should also meet the continuous conditions.Because the actual volatility is not directly observable,it is necessary to use specific models to characterize volatility and accurately predict it.For this reason,early modells such as ARCH model and SV model were proposed based on the low frequency volatility problem.These models have been widely used in early market research because they can achieve better results and better estimate and predict the volatility of financial markets.However,in recent decades,the advancement of financial markets along with computer technology(storage technology,computing power,etc.)and the widespread use of computers in the financial market have led to explosive growth in market data,whereby the concept of big data is born and widely used in financial market data capture,big data analysis,and market trading strategies like quantitative trading,the volatility research method based on low frequency data is no longer applicable.This prompted scholars to begin to study the volatility model applicable to high-frequency data,so that a class of implemented measures represented by realized volatility has emerged.The realized volatility has received more and more attention from the academic community due to its simple model and free calculation,and it is important that these implemented measures can be used as direct observations of volatility.However,what is ultimately achieved by these methods is the volatility of the day,even when using intraday high frequency data.Such daytime volatility is obviously unable to describe the intraday volatility model,and it cannot be applied to quantitative trading strategies.Therefore,this article is to study the intraday volatility problem from this perspective.The functional data analysis method can take the high-frequency data in each period of time(daily,weekly,etc.)as a function of time,and this data characteristic just coincides with the concept of volatility,and it can happen solve the problem of intraday volatility patterns that could not be solved in previous studies.Therefore,this paper applies the functional data analysis method,and uses the high-frequency data of the stock market index as the research object to study the intraday volatility.Firstly,the high-frequency data points of the stock market,namely the CSI 300 volatility data,are intra-day non-parametric fit,to construct functional intra-day volatility data,and then analyze and explain the intra-day volatility.Through the analysis of the intraday volatility of the CSI 300 Index,it is found that the intraday volatility of the index has an "N"character.This paper attempts to explain the possible reasons behind this feature.In order to verify these possible causes,this paper conducts a functional principal component analysis of intraday volatility and finds that these interpretive factors can indeed be established to some extent.At the same time,to explain the change of intraday volatility from the perspective of volume and price relationship,this paper introduces the intraday trading volume explanatory variables.The functional intraday volatility is modeled by a method of functional regression analysis,a concurrency model.Then,according to the functional statistical test,it is found that the interpretation of the intraday trading volume for the intraday volatility changes is statistically significant.Based on the analysis of the intraday volatility of the CSI 300 Index and the analysis of the volume and price,this paper conducts a time series analysis of the intraday volatility.The main purpose is to predict the intraday volatility,which can be applied to the high frequency trading of the stock market.In this part of the study,the ARH model,the ARHX model and the kernel model are respectively used to predict the functional intraday volatility,and then the prediction model is selected by comparing the prediction error of each angle and the prediction effect.Finally,according to the prediction results,it is found that the ARHX model has a relatively good predictive effect on the intraday volatility.This model is also a functional autoregressive model with the intraday volume of exogenous explanatory variables added.