High-Order Self-excited Threshold Integer-Valued Autoregressive Model: Estimation and Testing

Motivated by the need of modeling and inference for high-order integer-valued threshold time series models, this paper introduces a pth-order two-regime self-excited threshold integer-valued autoregressive (SETINAR(2, p)) model. Basic probabilistic and statistical properties of the model are discussed. The parameter estimation problem is addressed by means of conditional least squares and conditional maximum likelihood methods. The asymptotic properties of the estimators, including the threshold parameter, are obtained. A method to test the nonlinearity of the underlying process is provided. Some simulation studies are conducted to show the performances of the proposed methods. Finally, an application to the number of people suffering from meningococcal disease in Germany is provided.