The joint distribution of the maximum and minimum of an AR(1) process

Christopher S. Withers and Saralees Nadarajah

Statistics & Probability Letters, 2015, vol. 99, issue C, 77-84

Abstract: Consider a sequence of n observations from an autoregressive process of order 1 with maximum Mn and minimum mn. We give their joint cumulative distribution function first in terms of n repeated integrals and then, for the case, where the marginal distribution of the observations is absolutely continuous, as a weighted sum of nth powers of eigenvalues of a certain Fredholm kernel. This enables good approximations for the joint distribution when n repeated integrals is not a practical solution.

Keywords: Autoregressive process; Fredholm kernel; Joint distribution; Maximum; Minimum (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2015.01.007

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