Statistical Inference On The Calendar Effect Of Volatility In Financial Markets

The main research content of this paper is about the statistical inference on calendar effect of financial market volatility.Volatility has always been a very hot topic in the field of financial econometrics.In the past two decades,a large number of literatures have focused on the estimation and prediction of volatility,such as the proposal of realized volatility(RV),etc.Due to the development of computer,financial econometricians have a deeper understanding of volatility from only low-frequency financial data in the last century to high-frequency data or even ultra-high-frequency data now.Because a higher frequency of data relative to the low frequency data means that contains more information,but econometricians aware of high frequency financial data often contains microstructure noise,thus there are two scales realized volatility(TSRV),pre-averaged estimator(PAVE),the quasi maximum likelihood estimator(QMLE),and other methods to solve the problem of noise under the high frequency data,to estimate the volatility.Calendar effect is the phenomenon that the values of some indexes in the financial market show a certain regular trend corresponding to the time.For example,Cross(1973)studied the return of the S&P500 Index from 1953 to 1970 and found that the average return on Friday was always higher than the average return on Monday.Wood,Mc Inish and Ord(1985)and Harris(1986)stated in the paper that in a trading day,the volatility process is a significant”U”shaped,that is,the volatility process is relatively high at the opening and closing of the trading day,but low at noon.In view of this,it is necessary to propose the volatility calendar effect estimator and give the corresponding statistical inference.The specific content of this paper is arranged as follows:Chapter 1 elaborates the development of volatility estimation,the empirical dis-covery of calendar effect of volatility and the development of calendar effect modeling in detail.Then,it explains the significance and innovation of this work.In Chapter 2,assuming that prices obey the general semimtingale diffusion mod-el,we give the calendar effect estimators of a more general form,covering the esti-mators given by Andersen et al.(2019),and giving the consistency and asymptotic normality(consistency and central limit theorem in the functional sense)in the Sko-rokhod space.As far as we know,we firstly give a series of theory in the sense of this functional.In Chapter 3,we give asymptotic theory on the weighted~2space under a weaker assumption than that in Skorokhod space.Both the asymptotic theory in space is necessary,the asymptotic theory in Skorokhod space is mainly on the calendar effect estimator for finite dimensional statistical inference,such as constructing a confidence band,and so on,and the weighted~2space can be wholly infer the calendar effect function,such as calendar effect function test,etc.In Chapter 4,we give the calendar effect estimator in the semimartingale diffu-sion plus microstructure noise model,use the pre-average method to deal with the heteroscedasticity noise,and get the corresponding asymptotic theory.Further,we test whether the calendar effect in noise variance and the calendar effect in volatility are the same.Chapter 5 summarizes the thesis and gives the prospect of future research work.