Statistical Inference Of Time Series Models Under Missing Mechanism

In the field of complete data,the theories and methods of time series models have been quite rich and complete.Many processing methods are given in the establishment,parameter estimation and prediction of time series models.However,in practical problems,due to various reasons,data are often missing.If reasonable methods are not adopted,the information loss caused by missing will greatly reduce the effect of statistical inference.At this time,how to make reasonable statistical inference is our next research problem.At present,most of the missing problems are concentrated in the field of linear statistical models.There are not many studies on time series models.The analysis of time series models is more complex than linear statistical models.The research on non-stationary time series under missing mechanism is more rare.This paper analyzes the stationary time series and the non-stationary time series of hidden periodicity model.This paper focuses on the statistical inference of stationary time series of AR(p)model and non-stationary time series of hidden periodicity model under several missing mechanisms.By proposing reasonable and feasible estimator,the asymptotic properties of estimator,such as consistency and asymptotic normality,are mathematically proved.The correctness of the theory is verified from the perspective of numerical simulation,and the relevant applications of the theory are given through real data.It is significance to the theoretical research of time series under missing mechanism.In the part of the statistical inference of AR(p)model under missing mechanism,we mainly study the statistical inference methods of autoregression coefficient and noise variance of AR(p)model under missing mechanism.In the theoretical derivation,the moment estimation method is used to estimate the parameters,and the consistency and asymptotic normality of estimator are proved.Based on the theory of asymptotic normality,the corresponding interval estimation of autoregressive coefficients is given.The correctness of the theory is verified from the numerical simulation,and the practical application of the theory is given through real data analysis.In the part of the statistical inference of hidden periodicity model under the missing mechanism,we give the corresponding statistical inference methods for the angular frequency vectors,the number of angular frequencies and amplitudes.In the theoretical derivation,the order of the signal periodogram and the uniform upper bound of the noise periodogram of the hidden periodicity model under the missing mechanism are obtained,and the image of the periodogram of the hidden periodicity model after missing is obtained.Then,using the periodogram method and the corresponding algorithm,the estimators of angular frequency vector,number of angular frequencies and amplitude are given.The convergence speed of the estimators is proved.From numerical simulation,the correctness of parameter estimation theory is verified,and an empirical method for divided line’s threshold value of periodogram in hidden periodicity model is given.From the perspective of numerical simulation,compared with the complete data,the selection of the noise part of the hidden periodicity model under the missing mechanism needs more strict condition.Finally,we introduce the practical application of the theory.