Parameter change test for random coefficient integer‐valued autoregressive processes with application to polio data analysis

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Parameter Change Test for Poisson Autoregressive Models (2014, background): “Kang & Lee (2009) proposed a CUSUM test for detecting change points in random coefficient integer-valued autoregressive models with Poisson innovations and used it to analyse polio data.”
Interventions in log-linear Poisson autoregression (2012, background): “A close look at the data reveals that there might exist a long-term decrease of the incidence rate, see Zeger (1988), Li (1991), Fahrmeir and Tutz (2001, Chap.”
Parameter change test for zero-inflated generalized Poisson autoregressive models (2016, methodology): “From Proposition A.4, we can see that I(θ0) −1/2 1√ n ∂L̃[ns](θ0) ∂θ w−→ Bd+2(s), Further, using Egorov’s theorem and Proposition A.5 (cf. Lemma 9 of Kang and Lee [34]), we obtain max 1≤k≤n √ k n ‖̃k‖ = oP(1).”