Multiple Change Points by Filtered Derivative and False Discovery Rate

Abstract

Let X = (X1; X2; : : : ; Xn) be a time series, that is a sequence of random variable indexed by the time t = 1; 2; : : : ; n. We assume the existence of a segmentation T = (t1; t2; : : : ; tn) such that Xi is a family of independent identically distributed (i.i.d) random variable for i E (tk; tk + 1]; and k = 0; : : : ; K where by convention to and tK+1 = N. In the literature, it exist two main kinds of change points detection : The change points on-line and the change points off-line. In this work, we consider only the change point analysis ( off-line), when number of change points is unknown. The result obtained is based on Filtered Derivative method where we use a second step based on False Discovery Rate. We compare numerically this new method with the Filtered Derivative with p-Value. We also give a real application of the method of Filtered Derivative with False Discovery Rate (FDqV).