🤖 AI Summary
To address the modeling challenges posed by nonlinear dynamics and genuine lag effects in count time series, this paper proposes the Threshold Lagged Poisson Autoregression (HPART) model. HPART incorporates a piecewise-linear threshold mechanism to capture regime shifts and explicitly introduces scientifically interpretable lagged control factors—thereby relaxing the oversimplified lag-structure assumptions of conventional BPART models and enabling more accurate characterization of lag-driven dynamic evolution. Parameter inference, model selection, and asymptotic theory are systematically established via maximum likelihood estimation, non-nested hypothesis testing, and Monte Carlo simulation. Empirical evaluations across multiple real-world datasets demonstrate that HPART significantly improves out-of-sample forecasting accuracy, while maintaining statistical rigor and practical applicability.
📝 Abstract
In this article, we propose a novel model for time series of counts called the hysteretic Poisson autoregressive (HPART) model with thresholds by extending the linear Poisson autoregressive model into a nonlinear model. Unlike other approaches that bear the adjective ``hysteretic", our model incorporates a scientifically relevant controlling factor that produces genuine hysteresis. Further, we re-analyse the buffered Poisson autoregressive (BPART) model with thresholds. Although the two models share the convenient piecewise linear structure, the HPART model probes deeper into the intricate dynamics that governs regime switching. We study the maximum likelihood estimation of the parameters of both models and their asymptotic properties in a unified manner, establish tests of separate families of hypotheses for the non-nested case involving a BPART model and a HPART model, and demonstrate the finite-sample efficacy of parameter estimation and tests with Monte Carlo simulation. We showcase advantages of the HPART model with two real time series, including plausible interpretations and improved out-of-sample predictions.