The Different Asymptotic Regimes of Nearly Unstable Autoregressive Processes

Thibault Jaisson () and Mathieu Rosenbaum ()
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Thibault Jaisson: CMAP, École Polytechnique
Mathieu Rosenbaum: LPMA, Université Marie et Pierre Curie (Paris 6)

A chapter in The Fascination of Probability, Statistics and their Applications, 2016, pp 283-301 from Springer

Abstract: Abstract We extend the results of [14, 27, 29] about the convergence of nearly unstable AR(p) processes to the infinite order case. To do so, we proceed as in [19, 20] by using limit theorems for some well chosen geometric sums. We prove that when the coefficients sequence has a light tail, nearly unstable AR( $$\infty $$ ∞ ) processes behave as Ornstein-Uhlenbeck models. However, in the heavy tail case, we show that fractional diffusions arise as limiting laws for such processes.

Keywords: Autoregressive processes; AR( $$\infty $$ ∞ ); Nearly unstable processes; Limit theorems; Ornstein-Uhlenbeck processes; Fractional diffusions; Volatility modeling (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-25826-3_13

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DOI: 10.1007/978-3-319-25826-3_13

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