INARCH(1) processes: Higher-order moments and jumps

Christian H. Weiss (1)

1 Department of Mathematics

The INARCH(1) model is a simple but practically relevant, two-parameter model for processes of overdispersed counts with an autoregressive serial dependence structure. We derive closed-form expressions for the joint (central) moments and cumulants of the INARCH(1) model up to order 4. These expressions are applied to derive moments of jumps in INARCH(1) processes. We illustrate this kind of application with a real-data example, and outline further potential applications.

Mots clés: Count-data time series; Cumulants; INARCH(1) model; Jumps; moments; Overdispersion

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Christian H. Weiss. INARCH(1) processes: Higher-order moments and jumps. Statistics and Probability Letters, 2010, ⟨10.1016/j.spl.2010.08.001⟩. ⟨hal-00691785⟩