Nonlinear time series models are crucial for modeling nonlinear phenomena of counts. The present work introduces a multiplicative thinning-based integer-valued bilinear model which allows more flexibility for the new arrivals that treat independently. We shall recognize that this new model forms a bridge between the INAR model and a feature of the multiplicative thinning-based INARCH model. The proposed model is suitable for the data exhibits several sharp spikes which cannot be explained by any linear model. Important properties of the proposed model are derived. After considering some estimation methods based on time domain and frequency domain approaches, simulation studies are conducted to check the performance of the estimates. The analysis of practical cases in social science is accomplished to highlight the usefulness of the proposed model in app.
