Abstract: Firstly, aiming at the modelling problem of complex integer-valued time series data, we proposed a first-order mixed integer-valued binomial autoregressive model. Secondly, we proved the strict stationary ergodicity of the model, gave the probabilistic statistics properties of the model, such as transition probability, expectation and variance, and estimated the model parameters by maximum likelihood method. Finally, the proposed model was applied to the fitting of harmonised index of consumer price (HICP)  data. The example analysis results show that the fitting effect of the proposed model is better than that of the existing model.

Key words: integer-valued time series, first-order mixed , binomial autoregressive model, stationarity, maximum likelihood estimation