Goodness-of-Fit Test for Mismatched Self-Exciting Processes

• URL: http://arxiv.org/abs/2006.09439v3
• Date: Fri, 12 Feb 2021 16:33:13 GMT
• Title: Goodness-of-Fit Test for Mismatched Self-Exciting Processes
• Authors: Song Wei, Shixiang Zhu, Minghe Zhang, Yao Xie
• Abstract summary: We develop a GOF test for generative models of self-exciting processes by making a new connection to this problem with the classical statistical theory of Quasi-likelihood estimator (QMLE) We present a non-parametric self-normalizing statistic for the GOF test: the Generalized Score (GS) statistics, and explicitly capture the model misspecification when establishing the distribution of the GS statistic.
• Score: 18.892845399295254
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently there have been many research efforts in developing generative models for self-exciting point processes, partly due to their broad applicability for real-world applications. However, rarely can we quantify how well the generative model captures the nature or ground-truth since it is usually unknown. The challenge typically lies in the fact that the generative models typically provide, at most, good approximations to the ground-truth (e.g., through the rich representative power of neural networks), but they cannot be precisely the ground-truth. We thus cannot use the classic goodness-of-fit (GOF) test framework to evaluate their performance. In this paper, we develop a GOF test for generative models of self-exciting processes by making a new connection to this problem with the classical statistical theory of Quasi-maximum-likelihood estimator (QMLE). We present a non-parametric self-normalizing statistic for the GOF test: the Generalized Score (GS) statistics, and explicitly capture the model misspecification when establishing the asymptotic distribution of the GS statistic. Numerical simulation and real-data experiments validate our theory and demonstrate the proposed GS test's good performance.

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