论文标题
推断非组织时间序列的计数，并应用于更改点问题
Inference for nonstationary time series of counts with application to change-point problems
论文作者
论文摘要
我们考虑一个整数值时间序列$ y =（y_t）_ {t \ in \ z} $，其中$ k^*$之后的型号是poisson自动回旋，其条件平均值取决于参数$θ^*\inθ\inθ\ intim subset \ subset \ r^d $。 $ k^*$之前的过程的结构未知;它可能是其他任何整数值时间序列，也就是说，$ y $可能是非组织的。可以确定，在非组织观察结果上计算出的$θ^*$的最大似然估计器是一致的，并且渐近地正常。接下来，我们在大量的泊松自回归模型中执行顺序更改点检测。我们提出了一种监视方案，用于检测模型中的变化。该过程基于一个更新的估计器，该估计量是在没有历史观察结果的情况下计算的。尤其是研究了检测器的渐近行为，上述对非组织环境中推断的结果被应用以证明所提出的程序是一致的。提供了仿真研究以及真实的数据应用程序。
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 autoregressive models. We propose a monitoring scheme for detecting change in the model. The procedure is based on an updated estimator which is computed without the historical observations. The asymptotic behavior of the detector is studied, in particular, the above result on the inference in a nonstationary setting are applied to prove that the proposed procedure is consistent. A simulation study as well as a real data application are provided.
