A Graphical Method for Identifying Potential Domains for Change Points in Generalized Bernoulli Processes
by
Yan-Xia Lin
School of Mathematics and Applied Statistics, University of Wollongong, Australia

Consider a sequence of observations {y_t}_{t ≤ T} drawn from a generalized Bernoulli process which might have structure changes. In general, it is not efficient to estimate the change points by directly applying standard inference methods to {y_t}_{t ≤ T}. An example of showing the inefficiency is given in this paper. However, the efficiency of estimation can be significantly improved if a narrow potential domain of change points in testing data can be identified form the data before inference methods are applied to.

In this paper, we are interested in how to identify the potential domain of change points in a generalized Bernoulli process through graphical approach. It is well known that the information on the structure change of a generalized Bernoulli process is not easy to be identified through the time series plot of the process itself. Therefore, the concepts of associate process and second-layer process of a generalized Bernoulli process are introduced in this paper. Examples are used to demonstrate that, by utilizing the time series plots of the associate process or second-layer process, it is easier to discover whether there are any structure changes in a generalized Bernoulli process. This graphical method is named indirect plot of generalized Bernoulli processes. An application of this method to a DNA sequence presents in this paper.

Date received: February 10, 2008