Statistical analysis of point processes and associated marks

When we have some ultra-high-frequency data like stock transaction data, the process can be analyzed by Marked point processes. Engle (2000) proposes the ACD model for IBM stock transaction process and also brings forward some interesting problems about point processes and marked point processes, which lead to this thesis.;In this thesis, first I devise some useful properties for the finite Fourier transform of a point process with a cyclic intensity function. Then I propose the hypothesis testing of a cyclic intensity function. The test procedure and test statistic are given based on the properties. Simulation studies and application are done to illustrate the theory.;For the test of intensity shift of a point process, I make some assumptions, devise some quantities to detect the shift and obtain the limiting distribution of the quantities under different settings. The procedure of detection, simulations and applications are given to show the theoretical work.;Then I move on to the covariance structure shift of a point process and propose some hypothesis testing for the covariance stationarity. I also put forward a procedure for detection of change point of covariance structure of a point process, which can be generalized to other stochastic processes.;Finally I investigate the relationship between marks and point process and devise a way to test whether the dependence between marks and point process is significant based on the thinning property of a point process. Simulations and applications are done to show the work.