Poisson QMLE for change-point detection in general integer-valued time series models

Evolutionary Inference via the Poisson Indel Process

We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classical evolutionary process, the TKF91 model, is a continuous-time Markov chain model comprised of insertion, deletion and substitution events. Unfortunately this model gives rise to an intractable computational problem---the computation of the marginal likelihood under the TKF91 model is exponential in the number…

Poisson limit of an inhomogeneous nearly critical INAR(1) model

An inhomogeneous first--order integer--valued autoregressive (INAR(1)) process is investigated, where the autoregressive type coefficient slowly converges to one. It is shown that the process converges weakly to a Poisson or a compound Poisson distribution.

The asymptotic structure of nearly unstable non-negative integer-valued AR(1) models

This paper considers non-negative integer-valued autoregressive processes where the autoregression parameter is close to unity. We consider the asymptotics of this `near unit root' situation. The local asymptotic structure of the likelihood ratios of the model is obtained, showing that the limit experiment is Poissonian. To illustrate the statistical consequences we discuss efficient estimation of the autoregression parameter and efficient testing for a unit root.

Piecewise autoregression for general integer-valued time series

This paper proposes a piecewise autoregression for general integer-valued time series. The conditional mean of the process depends on a parameter which is piecewise constant over time. We derive an inference procedure based on a penalized contrast that is constructed from the Poisson quasi-maximum likelihood of the model. The consistency of the proposed estimator is established. From practical applications, we derive a data-driven procedure based on the slope heuristic to calibrate the penalty term of the contrast; and the implementation is carried out through the dynamic programming algorithm…

Discrete approximations for sums of m-dependent random variables

Sums of of 1-dependent integer-valued random variables are approximated by compound Poisson, negative binomial and Binomial distributions and signed compound Poisson measures. Estimates are obtained for total variation and local metrics. The results are then applied to statistics of $m$-dependent $(k_1,k_2)$ events and 2-runs. Heinrich's method and smoothing properties of convolutions are used for the proofs.

整数值移动平均随机场

The Integer-valued Moving-Average Random Field

提出并研究了计数随机场的整数值移动平均（INMA）模型，推导了其边际分布和空间依赖结构的闭式表达式，并展示了泊松边际分布和多种依赖结构的可能性。

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

We consider an integer-valued time series $Y=(Y_t)_{t\in\Z}$ where the models after a time $k^*$ is Poisson autoregressive with the conditional mean that depends on a parameter $θ^*\inΘ\subset\R^d$. The structure of the process before $k^*$ is unknown;? it could be any other integer-valued time series, that is, the process $Y$ could be nonstationary.? It is established that the maximum likelihood estimator of $θ^*$ computed on the nonstationary observations is consistent and asymptotically normal. Next, we carry out the sequential change-point detection in a large class of Poisson autoregressi…

混合差分整值GARCH模型用于$ \mathbb{Z}$-valued时间序列

Mixed difference integer-valued GARCH model for $ \mathbb{Z}$-valued time series

本文提出一种灵活的观测驱动Z-valued时间序列模型，通过混合负数和非负数分量实现更广泛的适用性，支持偏态和双峰性，同时简化了解释与分析，并通过模拟和实证验证了方法的有效性。

The tempered discrete Linnik distribution

A tempered version of the discrete Linnik distribution is introduced in order to obtain integer-valued distribution families connected to stable laws. The proposal constitutes a generalization of the well-known Poisson-Tweedie law, which is actually a tempered discrete stable law. The features of the new tempered discrete Linnik distribution are explored by providing a series of identities in law - which describe its genesis in terms of mixture and compound Poisson law, as well as in terms of mixture discrete stable law. A manageable expression of the corresponding probability function is also…