Asymptotic behavior of unstable INAR(p) processes

By Mátyás Barczy, Marton Ispany, Gyula Pap. 2009

47 citations recorded by the source corpus.

In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR(p)) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from an unstable INAR(p) process converges weakly towards a squared Bessel process. We note that this limit behavior is quite different from that of familiar unstable autoregressive processes of order p. An application for Boston armed robberies data set is presented.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/012f5ee7f42e524c5e7d27c372489499bb6987d5

How researchers see this paper

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In Artificial Intelligence

1. Mathieu Rosenbaum

In Finance

1. Mathieu Rosenbaum
2. Thibault Jaisson
3. Omar El Euch
4. Eduardo Abi Jaber
5. Paul Jusselin
6. Jim Gatheral
7. Christa Cuchiero
8. Emmanuel Bacry

In Statistics and Probability

1. Mathieu Rosenbaum
2. Alexandre B. Tsybakov
3. David J. Biagioni
4. Xinbing Kong

Citations in the corpus

• Limit theorems for nearly unstable Hawkes processes (2013, background): “• In the classical time series setting let us mention the paper [8] where the authors study the asymptotic behavior of unstable integer-valued autoregressive model (INAR processes).”