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A threshold mixed count time series model: estimation and application

Mardi Dungey , Vance L. Martin EMAIL logo , Chrismin Tang and Andrew Tremayne


A new class of integer time series models is proposed to capture the dynamic transmission of count processes over time. The approach extends existing integer mixed autoregressive-moving average models (INARMA) by allowing for shifts in the dynamics of the count process through regime changes, referred to as a threshold integer autoregressive-moving average model (TINARMA). An efficient method of moments estimator is proposed, with standard errors based on subsampling, as maximum likelihood methods are infeasible for TINARMA processes. Applying the framework to global banking crises over 200 years of data, the empirical results show strong evidence of autoregressive and moving average dynamics which vary across systemic and nonsystemic regimes over time. Coherent forecast distributions are also produced with special attention given to the Great Depression and the more recent Global Financial Crisis.

JEL Classification: C150; C220; C250

Award Identifier / Grant number: DP14012137

Funding statement: Funder Name: Australian Research Council, Funder Id: 10.13039/501100000923, Grant Number: DP14012137.


We would like to thank the editor and an anonymous referee for insightful comments and suggestions which improved the paper.


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Published Online: 2019-03-26

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