Inference for nonstationary time series of counts with application to change-point problems

  title={Inference for nonstationary time series of counts with application to change-point problems},
  author={William Kengne and Isidore S'eraphin Ngongo},
  journal={Annals of the Institute of Statistical Mathematics},
We consider an integer-valued time series $$(Y_t)_{t\in {\mathbb {Z}}}$$ ( Y t ) t ∈ Z where the model after a time $$k^*$$ k ∗ is Poisson autoregressive with the conditional mean that depends on a parameter $$\theta ^*\in \varTheta \subset {\mathbb {R}}^d$$ θ ∗ ∈ Θ ⊂ R d . The structure of the process before $$k^*$$ k ∗ is unknown; it could be any other integer-valued process, that is, $$(Y_t)_{t\in {\mathbb {Z}}}$$ ( Y t ) t ∈ Z could be nonstationary. It is established that the maximum… 
Poisson QMLE for change-point detection in general integer-valued time series models
We consider together the retrospective and the sequential change-point detection in a general class of integer-valued time series. The conditional mean of the process depends on a parameter $$\theta


Monitoring procedure for parameter change in causal time series
Piecewise autoregression for general integer-valued time series
Poisson Autoregression
In this article we consider geometric ergodicity and likelihood-based inference for linear and nonlinear Poisson autoregression. In the linear case, the conditional mean is linked linearly to its
Testing for parameter constancy in general causal time‐series models
We consider a process belonging to a large class of causal models including AR(∞), ARCH(∞), TARCH(∞),… processes. We assume that the model depends on a parameter and consider the problem of testing
Modified sequential change point procedures based on estimating functions
Abstract: A large class of sequential change point tests are based on estimating functions where estimation is computationally efficient as (possibly numeric) optimization is restricted to an initial
Testing Parameter Change in General Integer‐Valued Time Series
We consider the structural change in a class of discrete valued time series, which the conditional distribution belongs to the one‐parameter exponential family. We propose a change point test based
Poisson QMLE of Count Time Series Models
Regularity conditions are given for the consistency of the Poisson quasi‐maximum likelihood estimator of the conditional mean parameter of a count time series model. The asymptotic distribution of
Parameter Change Test for Poisson Autoregressive Models
In this paper, we consider the problem of testing for a parameter change in Poisson autoregressive models. We suggest two types of cumulative sum (CUSUM) tests, namely, those based on estimates and
Monitoring parameter change in AR(p) time series models