Tobit models for count time series
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计数时间序列的 Tobit 模型
- 研究问题
- 如何在计数时间序列中同时实现近似线性结构与负自相关，并将方法扩展到无界计数、有界计数及不同整数值模型？
- 方法与思路
- 作者提出 Tobit 构造，详细研究 Skellam–Tobit INGARCH 的平稳性、矩近似、极大似然和删失最小绝对偏差估计，并讨论扩展。
- 材料陈述的贡献
- 摘要称 Tobit 方法较 softplus 方法适用范围更广，提供理论分析、估计模拟及三个实际数据例子，展示负自相关计数建模的用途。
- 阅读关注点
- 应核对 Tobit 构造与负自相关形成机制、平稳性条件及矩近似误差，并区分详细研究的模型与仅讨论的有界计数等扩展。
- 阅读边界
- 这是 arXiv 预印本，未核实同行评审或期刊接收。摘要未给出参数限制、估计性质和比较数值，不能判断所有扩展均已充分验证。
原文摘要
Several models for count time series have been developed during the last decades, often inspired by traditional autoregressive moving average (ARMA) models for real-valued time series, including integer-valued ARMA (INARMA) and integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models. Both INARMA and INGARCH models exhibit an ARMA-like autocorrelation function (ACF). To achieve negative ACF values within the class of INGARCH models, log and softplus link functions are suggested in the literature, where the softplus approach leads to conditional linearity in good approximation. However, the softplus approach is limited to the INGARCH family for unbounded counts, i.e. it can neither be used for bounded counts, nor for count processes from the INARMA family. In this paper, we present an alternative solution, named the Tobit approach, for achieving approximate linearity together with negative ACF values, which is more generally applicable than the softplus approach. A Skellam--Tobit INGARCH model for unbounded counts is studied in detail, including stationarity, approximate computation of moments, maximum likelihood and censored least absolute deviations estimation for unknown parameters and corresponding simulations. Extensions of the Tobit approach to other situations are also discussed, including underlying discrete distributions, INAR models, and bounded counts. Three real-data examples are considered to illustrate the usefulness of the new approach.