We propose a semi-parametric self-exciting point process model for independent n string observations. The intensity process consists of an unspecified time varying baseline and a parametric excitation function. The associated martingale estimating equations are constructed to get a desirable estimator. Under certain regularity conditions, the consistency and asymptotically normal of the estimator for the parametric excitation function are established based on counting process martingale central limit theory. Meanwhile, the Breslow type estimator for the non-parametric baseline is proved to converge weakly to a mean zero Gaussian Process. We do simulation to verify the efficiency of the estimating method and present its applications in the financial data analysis.

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We propose a semi-parametric self-exciting point process model for independent n string observations. The intensity process consists of an unspecified time varying baseline and a parametric excitation function. The associated martingale estimating equations are constructed to get a desirable estimator. Under certain regularity conditions, the consistency and asymptotically normal of the estimator for the parametric excitation function are established based on counting process martingale central limit theory. Meanwhile, the Breslow type estimator for the non-parametric baseline is proved to converge weakly to a mean zero Gaussian Process. We do simulation to verify the efficiency of the estimating method and present its applications in the financial data analysis.

Keywords: Counting process martingale; Self-exciting process; Time-varying background; Asymptotic normal; Consistency.