Sequential change-point detection for time series enables us to sequentially check the hypothesisthat the model still holds as more and more data are observed. It’s widely used in data monitoring in practice. In this work, we propose two models: Binomial AR(1) model and Generalized Beta AR(p) model, for modeling binomial time series and compositional time series, respectively. For each model, we prove that a process following the model is stationary and ergodic. When the model order is p = 1, we show the partial MLE of each model is consistent and asymptotically normal. We propose parametric sequential change-point detection methods to detect any parameter-related changes for the two models when the model orders p = 1. For Generalized Beta AR model with any model order p = 1, 2, . . . , we propose a nonparametric sequential changepoint detection method that is able to detect any distributional changes, not limited to parameter changes. The limiting behaviors of the test statistics of the methods are investigated. The powers of the tests are also analyzed. The abilities of the methods to successfully detect change points are shown in applications.

Creator

• Liu, Yajun

DOI

• https://doi.org/10.21985/n2-xhcf-9a06

Subject

• Statistics

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:16079
• etdadmin_upload_902877

Keyword

• compositional time series
• time series of counts
• ergodicity
• strong mixing processes
• sequential change-point detection

Date created

• 2022-01-01

Resource type

• Dissertation

Rights statement

• In Copyright