Moments of Maximum: Segment of AR(1)

08/12/2019

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by   Steven Finch, et al.

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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 ρ be the lag-one serial correlation, which satisfies |ρ| < 1. For what value of ρ is E(M) maximized? How does V(M) behave for increasing ρ? Answers to these questions lie in Afonja (1972), suitably decoded.