2025/06/03 by Deschatre, Thomas, Gruet, Pierre, Lotz, Antoine
#60G55 #62F03 #62F12 #FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2506.02631
We consider the problem of estimating the parameters of a non-stationary Hawkes process with time-dependent reproduction rate and baseline intensity. Our approach relies on the standard maximum likelihood estimator (MLE), coinciding with the conventional approach for stationary point processes characterised by [Ogata, 1978]. In the fully parametric setting, we find that the MLE over a single observation of the process over [0, T] remains consistent and asymptotically normal as T → ∞. Our results extend partially to the semi-nonparametric setting where no specific shape is assumed for the reproduction rate g \colon [0, 1] ↦ ℝ+. We construct a time invariance test with null hypothesis that g is constant against the alternative that it is not, and find that it remains consistent over the whole space of continuous functions of [0, 1]. As an application, we employ our procedure in the context of the German intraday power market, where we provide evidence of fluctuations in the endogeneity rate of the order flow.