Change‐Point Detection in Autoregressive Models with no Moment Assumptions

Abstract

In this paper we consider the problem of detecting a change in the parameters of an autoregressive process where the moments of the innovation process do not necessarily exist. An empirical likelihood ratio test for the existence of a change point is proposed and its asymptotic properties are studied. In contrast to other works on change‐point tests using empirical likelihood, we do not assume knowledge of the location of the change point. In particular, we prove that the maximizer of the empirical likelihood is a consistent estimator for the parameters of the autoregressive model in the case of no change point and derive the limiting distribution of the corresponding test statistic under the null hypothesis. We also establish consistency of the new test. A nice feature of the method is the fact that the resulting test is asymptotically distribution‐free and does not require an estimate of the long‐run variance. The asymptotic properties of the test are investigated by means of a small simulation study, which demonstrates good finite‐sample properties of the proposed method.

Investigation of Filtering and Objects Detection Algorithms for a Multizone Image Sequence

“…The developed algorithm provides better results also in comparison with usual autoregression (Akashi 2016, Baragona 2015. Figure 5 (X-axis is Signal-to-Noise Relation, Y-axes is Correct Detection Probability) shows graphs of the probability of correct detection as a function of the signal-to-noise ratio.…”

Adaptive Quantile Computation for Brownian Bridge in Change-Point Analysis

“…with t k = k/n, which has been used by, e.g., Eastwood and Eastwood (1998) and Orasch and Pouliot (2004), and for a similar problem by Akashi, Dette, and Liu (2018).…”

A review on minimax rates in change point detection and localisation

“…Quite the contrary, the study of the fundamental limits of the testing problem is lagged behind. The literature on different aspects of testing includes Yao and Au (1989), Frick et al (2014), Enikeeva et al (2019), Vanegas et al (2019), Dette and Kutta (2019), Dette et al (2018a), Akashi et al (2018), Dette et al (2018c), Aue et al (2018), Aue and Horváth (2013), Robbins et al (2011), Liu et al (2019, Stoehr et al (2020), Kirch et al (2015), Jewell et al (2019), Chen (2019a), Jirak (2015), Chu and Chen (2019) and Verzelen et al (2020), among others.…”