Nonparametric estimation of counting process intensity function and its applications
Abstract: We propose estimators for the counting process intensity function and its derivatives by maximizing the local partial likelihood. We prove the consistency and asymptotic normality of the prosed estimators. In addition to the computational ease, a nice feature of the proposed estimators is the automatic boundary bias correction property. We also discuss the choice of the tuning parameters in the definition of the estimators. An effective and easy-to-calculate data-driven bandwidth selector is proposed. A small simulation experiment is carried out to assess the performance of the proposed bandwidth selector and the estimators. The estimator is apply to estimate the intra-day trading intensity of an ASX share. The results indicates a positive relationship between trading intensity and return volatility.
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