Moments of Maximum: Segment of AR(1)

Abstract

Let $X_t$ denote a stationary first-order autoregressive process. Consider five contiguous observations (in time $t$) of the series (e.g., $X_1,...,X_5$). Let $M$ denote the maximum of these. Let $\rho$ be the lag-one serial correlation, which satisfies $|\rho |<1$. For what value of $\rho$ is $\mathbb{E}(M)$ maximized? How does $\mathbb{V}(M)$ behave for increasing $\rho$? Answers to these questions lie in Afonja (1972), suitably decoded.

14 pages, 2 figures

References in corpus (4)

• Another Look at AR(1)
• Expected n-Step Product for Gaussian Tours
• Capturing, Ordering and Gaussianity in 2D
• The distribution of the maximum of a second order autoregressive process: the continuous case

Cited by in corpus (1)

• Number of Sign Changes: Segment of AR(1)