# Multiple Change Points by Filtered Derivative and False Discovery Rate

Let X = (X1; X2; : : : ; Xn) be a time series, that is a sequence of random variable indexed by thetime t = 1; 2; : : : ; n. We assume the existence of a segmentation τ = (τ1; τ2; : : : ; τn) such that Xi is a family of independent identically distributed (i.i.d) random variable for i ∈ (τk; τk + 1]; and k = 0; : : : ; K where by convention τo and τK+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 paper, we only look at change point analysis (off-line) when the number of change points is unknown. The obtained result is based on the Filtered Derivative method, with a second step based on the False Discovery Rate. This new method is numerically compared to the Filtered Derivative with p-Value. We also present a real-world application of the Filtered Derivative with False Discovery Rate method (FDqV).

**Author (s) Details**

**Mohamed Elmi
**Research Laboratory in Mathematics and Economics (LME), University Djibouti, Republic of Djibouti

**View Book : https://stm.bookpi.org/TPMCS-V11/article/view/1320**