Birnbaum-Saunders and Lognormal Kernel Estimators for Modelling Durations in High Frequency Financial Data

Xiaodong Jin

and

Janusz Kawczak

In this article we extend the class of non-negative, asymmetric kernel density estimators and propose Birnbaum-Saunders (BS) and lognormal (LN) kernel density functions. The density functions have bounded support on [0, ). Both BS and LN kernel estimators are free of boundary bias, non-negative, with natural varying shape, and achieve the optimal rate of convergence for the mean integrated squared error. We apply BS and LN kernel density estimators to high frequency intraday time duration data. The comparisons are made on several nonparametric kernel density estimators. BS and LN kernels perform better near the boundary in terms of bias reduction.

Key Words: Birnbaum-Saunders kernel; Lognormal kernel; High frequency; ACD model; Durations.
JEL Classification Numbers: C13, C14, C15, C41.