First-order Markov-switching integer-valued autoregressive process with signed binomial thinning

Traditional integer-valued autoregressive models are restricted to non-negative integers' assumption, which cannot handle overdispersion, piecewise nonlinear Z-valued time series. To capture Z-valued time series showing nonlinear features such as piecewise and over-dispersion, a class of Z-valued autoregressive models with Markov-switching coefficients based on the signed binomial thinning operator is considered. The proposed model extends the traditional Markov-switching integer-valued autoregressive model by allowing for negative values and more flexible dynamics. Basic probabilistic and statistical properties, including stationarity and moment properties, are derived. Conditional least squares and conditional maximum likelihood estimators are developed for parameter estimation. A comprehensive Monte Carlo simulation study is conducted to examine the finite sample performance of the estimation procedures. The practical utility of the proposed model is demonstrated through empirical applications.