Publication at Faculty of Mathematics and Physics |
2011
Abstract
Let $\{X_t,\ t \in \mathbb{Z}\}$ be a sequence of iid random variables with an absolutely continuous distribution. Let $a }0$ and $c\in\mathbb{R}$ be some constants.
We consider a sequence of 0-1 valued variables $\{\xi_t,\ t\in\mathbb{Z}\}$ obtained by clipping an MA(1) process $X_t-aX_{t-1}$ at the level $c$, i.e., $\xi_{t}=\mathsf{I}[X_t-aX_{t-1} {c]$ for all $t \in \mathbb{Z}$. We deal with the estimation problem in this model.
Properties of the estimators of the parameters $a$ and $c$, the success probability $p$, and the 1-lag autocorrelation $r_1$ are investigated. A numerical study is provided as an illustration of the theoretical results.