Joint semi-parametric INAR bootstrap inference for model coefficients and innovation distribution

2025-07-15

AI Summary

Semi-parametric inference for integer-valued autoregressive (INAR) models in count time series—simultaneously estimating model coefficients and the innovation distribution without parametric assumptions on the latter—remains challenging for diagnostics, forecasting, and goodness-of-fit assessment. Method: This paper proposes a novel semi-parametric INAR bootstrap method grounded in the binomial thinning mechanism. It enables joint asymptotically consistent self-bootstrapping of both coefficients and the innovation distribution without strong distributional assumptions. Contribution/Results: Theoretical analysis establishes its asymptotic validity, while simulations and empirical studies demonstrate robust finite-sample performance. The method delivers reliable inference, model diagnostics, and predictive evaluation across diverse discrete innovation distributions, markedly enhancing flexibility and practical applicability compared to existing approaches.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

For modeling the serial dependence in time series of counts, various approaches have been proposed in the literature. In particular, models based on a recursive, autoregressive-type structure such as the well-known integer-valued autoregressive (INAR) models are very popular in practice. The distribution of such INAR models is fully determined by a vector of autoregressive binomial thinning coefficients and the discrete innovation distribution. While fully parametric estimation techniques for these models are mostly covered in the literature, a semi-parametric approach allows for consistent and efficient joint estimation of the model coefficients and the innovation distribution without imposing any parametric assumptions. Although the limiting distribution of this estimator is known, which, in principle, enables asymptotic inference and INAR model diagnostics on the innovations, it is cumbersome to apply in practice. In this paper, we consider a corresponding semi-parametric INAR bootstrap procedure and show its joint consistency for the estimation of the INAR coefficients and for the estimation of the innovation distribution. We discuss different application scenarios that include goodness-of-fit testing, predictive inference and joint dispersion index analysis for count time series. In simulations, we illustrate the finite sample performance of the semi-parametric INAR bootstrap using several innovation distributions and provide real-data applications.

Problem

• Estimating INAR coefficients and innovation distribution semi-parametrically
• Developing bootstrap method for joint inference in count time series
• Enabling model diagnostics without parametric assumptions

Innovation

• Semi-parametric INAR bootstrap for joint estimation
• Consistent estimation without parametric assumptions
• Goodness-of-fit testing and predictive inference