Research On Intraday Volatility Of The Chinese Stock Market Based On Functional Data Analysis

In the financial markets,volatility has always been a hot topic in the financial field because volatility is critical to economic and financial decision making,portfolio allocation,financial product pricing and risk management.According to the theory of financial volatility,the volatility in practice changes with time,that is,it is random.Thus,it is very important to construct a model that can characterize volatility and accurately predict volatility.Since volatility is a variable that cannot be directly observed,this problem deeply affects the measurement of the volatility.In order to solve this problem,the early model based on the low frequency observed data,such as GARCH and the SV model have achieved great success in estimating and predicting the volatility and characterizing the fluctuation characteristics.Recent years,the development of financial market is very fast,and the research based on low frequency data has been difficulty to meet the requirements of the development of financial markets,so people turn to the research of high-frequency data or ultra-high-frequency data.For the research of high-frequency data,the traditional methods for low-frequency data may not obtain good results.This encourages researchers to begin studying the volatility models that fit high frequency data.At this point,realized volatility(RV)is one of the realized measures(RM),is welcomed by the researchers because of its no requirement of model and easy to calculation.It is important that these realized measures can be used as direct observations of volatility.Based on these realized measures,the HARRV model is established to describe the evolution of the volatility and to predict volatility in the future.However,these methods,although the use of intraday high-frequency data,but the daytime volatility is obtained.Obviously,such a daytime volatility is certainly not able to describe the volatility of the intraday volatility model.Functional data analysis treats the intra-day high-frequency transaction data as a random function of time,which coincides with the volatility of the time-varying and random characteristics.In view of this,this article considers intra-day 5 minutes high-frequency trading data of the Shanghai and Shenzhen 300(CSI 300)index(year 2015)as an example to explore three issues of the volatility for the Chinese stock market from the intra-day level.Firstly,the intra-day estimation data of the volatility are extracted from the intraday price data by using the function-based volatility process in the existing literature,and the characteristic taken from the intra-day changing pattern of the fluctuation rate and the volume is analyzed by the functional principal component analysis.Secondly,the relationship between intraday volatility and intraday trading volume is studied by using functional correlation analysis and function linear regression analysis.Finally,the prediction of intraday volatility and the real-time dynamic updating problem are studied based on the functional time series analysis method.A series of functional data analysis of the intra-day high frequency data of 5 minutes in the CSI 300 index(year 2015)is given,and the conclusion of this paper is given at the intraday level.Firstly,by functional principal component analysis(FPCA)we can find that the volatility shows a typical "calendar effect" from the intra-day data,that is,the high volatility data usually appear in the opening and closing time.There are four principal components that can be used to describe the intraday changing pattern of volatility,respectively.In general,the four principal components pattern can be seen as that,the volatility often reaches the peak in the morning,decreases before the closed time in the afternoon and after the open time in the morning,and also the volatility will reach the valley one hour after the open time in the afternoon.Secondly,by functional principal component analysis(FPCA)we can find that the intraday logarithmic volume shows a "U" shape.Using three principal components to describe the intraday changing pattern of the trading volume.Specifically,the first principal component curve highlights the change in volume after the open time in the morning,that is,the volume at the open time is relatively high,and then gradually decreased until midday close;the second main component curve highlights the change in volume before the close time in the afternoon,that is,the volume gradually increased after the open time in the afternoon,then increased to a relatively high level before the close time;and the third main component of the curve described the change in the volume one hour around the noon break,showing a decreasing trend in the first and then an increasing trend.The scatter points patterns between each two of the three principal components scores confirm the intraday changing pattern of the logarithmic volume of the three principal components.Thirdly,the relationship between the intraday volatility and the logarithmic volume of the CSI 300 index(year 2015)is analyzed by using the functional canonical correlation analysis(FCCA).The empirical results show that there is a linear correlation between the two objects considered.Then,the linear regression model(parallel model)is used to model the intraday volatility and logarithmic volume data.It is found that there is a positive correlation between the intraday volatility and the volume of the Shanghai and Shenzhen 300 index.Fourthly,through the functional time series analysis(FTSA)to study the short-term forecast of volatility in the CSI 300 Index.Functional time series analysis uses the volatility function in terms of temporal dependency to improve the accuracy of short-term prediction of volatility.The results of empirical analysis show that the ARIMA model based on the principal component regression is slightly higher than the prediction accuracy of the VAR model,when point prediction and interval prediction are considered for intraday volatility.In addition,the dynamic update of the volatility of half-day in the afternoon can be predicted by using the observed half-day price data in the morning.The results of empirical analysis show that the error of the updated point prediction and interval prediction given by the functional linear regression(FLR)are smaller than that given by the block moving method(BM).