mloglik1d: Minus loglikelihood of an IHSEP model In IHSEP: Inhomogeneous Self-Exciting Process

Description

Calculates the minus loglikelihood of an IHSEP model with given baseline intensity function ν and excitation function g(x)=∑ a_i exp(-b_i x) for event times jtms on interval [0,TT].

Usage

 1 mloglik1d(jtms, TT, nu, gcoef, Inu)

Arguments

 jtms A numeric vector, with values sorted in ascending order. Jump times to fit the inhomogeneous self-exciting point process model on. TT A scalar. The censoring time, or the terminal time for observation. Should be (slightly) greater than the maximum of jtms. nu A (vectorized) function. The baseline intensity function. gcoef A numeric vector (of 2k elements), giving the parameters (a_1,...,a_k,b_1,...,b_k) of the exponential excitation function g(x)=∑_{i=1}^k a_i*exp(-b_i*x). Inu A (vectorized) function. Its value at t gives the integral of the baseline intensity function ν from 0 to t.

Details

This function calculates the minus loglikelihood of the inhomegeneous Hawkes model with background intensity function ν(t) and excitation kernel function g(t)=∑_{i=1}^{k} a_i e^{-b_i t} relative to continuous observation of the process from time 0 to time TT. Like mloglik1c, it takes advantage of the Markovian property of the intensity process and uses external C++ code to speed up the computation.

Value

The value of the negative log-liklihood.

Author(s)

Feng Chen <feng.chen@unsw.edu.au>