Observation‐Driven Random Coefficient Threshold INAR Models for Count Time Series

ABSTRACT This paper introduces a new class of observation‐driven random coefficient integer‐valued autoregressive (ODRCMTTINAR) models featuring mixed thinning mechanisms and threshold effects. Unlike existing models that assume constant coefficients or purely deterministic dynamics, the proposed framework provides a key methodological contribution by modelling the autoregressive coefficient as a general function of past observations, allowing it to vary in a flexible manner with the data. This functional specification captures both structural regime changes and unobserved stochastic shocks by incorporating random error terms. Parameter estimation is conducted using conditional least squares (CLS) and conditional maximum likelihood (CML) methods under both known and unknown threshold scenarios. We establish the consistency and asymptotic normality of the proposed estimators. Simulation studies evaluate the finite‐sample performance of the models. Two empirical applications on stock trading volumes and crime counts further illustrate the effectiveness of the proposed approach in capturing the complex dynamics of count time series.