Study On Several Models With Conditional Heteroskedasticity Being Driven By Observed Series

In 1982,Engle,the Nobel Prize winner,groundbreakingly proposed the ARCH model.After that,Bollerslov extended it to a more general formalization and proposed GARCH model in 1986.The(G)ARCH type conditional heteroskedasticity models attracted great attention by experts in statistics and financial econometrics during the past several decades,and have been widely used in the theoretical and application research of financial time series analysis.In 2007,professor Shiqing Ling,presented the double autoregressive(DAR)model,and in his classical academic paper,he proved that the quasi maximum likelihood estimator(QMLE)of the model can also keep asymptotic normality without assumption of the second moment conditions for observed time series.Just like Ling predicted in his paper,the novel theoretical result of DAR model provides lots of insights in conditional heteroskedasticity model research field.Note that,the conditional variance in the DAR model is driven by lagged observable sequence,which is different from Engle's original ARCH model where the conditional variance is a quadratic function of lagged unobserved errors sequence.Due to the theoretical innovation of DAR model,in this thesis,we study several conditional heteroskedasticity models with conditional variances being driven by observable series.The main contents of this thesis include the following three aspects:Firstly,we extend the DAR model by letting the order goes to infinity,and study a moving average model with an alternative GARCH-type error.The quasi maximum likelihood estimator(QMLE)is shown to be asymptotically normal,without any strong moment conditions.Secondly,we study a vector double autoregressive(VDAR)model with conditional covariance matrix is determined by the observed series,which is a straightforward extension from univariate case to multivariate case of the DAR model.Sufficient ergodicity conditions are first given for the model.Without assuming the existence of second order moment conditions for observed time series,we establish the asymptotic theroy of the quasi maximum likelihood estimator(QMLE)for the parameter.Thirdly,a multivariate extension of a classical semiparametric GARCH-M model is discussed,and we call it multivariate partially linear GARCH-M model,in which the conditional covariance matrix is determined by the observed series.Estimators for both parameters and nonparametric functions are given basing on the profile likelihood approach.For all models considered above,simulations are conducted to assess the performance of the estimators,and the results show that the proposed methods perform well in finite sample.Illustrations based on real data sets are also considered,and they demonstrate that all the models we studied in this thesis have comparable or better fitting performance and predictive ability as comparing to the classical baseline models,which further implies that our models have potential valuable application value in practice..