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Testing Epidemic Change in Nearly Nonstationary Process with Statistics Based on Residuals by Markevičiūtė, Jurgita; Račkauskas, Alfredas; Suquet, Charles is a scholarly article available to read on EtoBox.

What is Testing Epidemic Change in Nearly Nonstationary Process with Statistics Based on Residuals about?

We study an epidemic type change in innovations of a first order autoregressive process $ y_{n,k} = \varphi_n y_{n,k-1} + \epsilon_{k} + a_{n,k}$, where $\phi_n$ is either a constant in $(-1,1)$ or a sequence in $(0,1)$, converging to 1. For $k$ inside some unknown interval $\mathbb{I}_n^\ast=(k^\ast,k^\ast+\ell^\ast]$, $a_{n,k}=a_n$ while $a_{n,k}=0$ for $k$ outside $\mathbb{I}_n^\ast$. When $a_n\neq 0$, we have an epidemic deviation from the usual (zero) mean of innovations. Since innovations are not observed, we build uniform increments statistics on residuals $(\widehat{\epsilon}_k)$ of the process $y_{n,k}$. We assume that innovations $(\epsilon_k)$ are regularly varying with index $p \ge 2$ or satisfies integrability condition $\lim_{t \to \infty} t^p P(|\epsilon_1| > t) = 0$ for $p > 2$ and $E\epsilon_k^2 < \infty$ for $p=2$. We find the limit distributions of the tests under no change and prove consistency under short epidemics that is $\ell^\ast=O(n^\beta)$ for some $0<\beta\le 1/2$.

Author

Markevičiūtė, Jurgita; Račkauskas, Alfredas; Suquet, Charles

Published

2014

Language

EN