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Asymptotics for moving average processes with dependent innovations

✍ Scribed by Qiying Wang; Yan-Xia Lin; Chandra M. Gulati

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
122 KB
Volume
54
Category
Article
ISSN
0167-7152

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✦ Synopsis

Let Xt be a moving average process deÿned by Xt = ∞ k=0 k t-k ; t = 1; 2; : : : , where the innovation { k } is a centered sequence of random variables and { k } is a sequence of real numbers. Under conditions on { k } which entail that {Xt} is either a long memory process or a linear process, we study asymptotics of the partial sum process [ns] t=0 Xt. For a long memory process with innovations forming a martingale di erence sequence, the functional limit theorems of [ns] t=0 Xt (properly normalized) are derived. For a linear process, we give su cient conditions so that [ns] t=1 Xt (properly normalized) converges weakly to a standard Brownian motion if the corresponding [ns] k=1 k is true. The applications to fractional processes and other mixing innovations are also discussed.

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Extremes of sub-sampled integer-valued m
Extremes of sub-sampled integer-valued moving average models with heavy-tailed innovations
✍ A. Hall; M.G. Scotto πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 206 KB

Let {X k } be a non-negative integer-valued stationary moving average sequence and deΓΏne Y k = X Tk as the sub-sampled series at a ΓΏxed integer interval T ΒΏ 1. We look at the limiting distribution of sample maxima of {Y k } and the corresponding extremal index.