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摘要翻译：
本文研究了区分单位根模型和各种爆炸模型的信息准则（如AIC、BIC、HQIC）的极限性质。爆炸模型包括局部到单位根模型、轻度爆炸模型和规则爆炸模型。考虑了不同数量级的初始条件。研究了OLS估计和间接推理估计。研究发现，当数据来自单位根模型时，BIC和HQIC一致选择单位根模型，而AIC不一致。当数据来自局部到单位根模型时，BIC和HQIC选择错误模型的概率都接近1，而AIC在极限范围内选择正确模型的概率为正。当数据来自常规爆炸模型或以$1+n^{\alpha}/n$with$\alpha\in(0,1)$形式的轻度爆炸模型时，三个信息准则一致地选择真实模型。间接推理估计可以根据信息准则和真实模型的不同，相对于OLS渐近地增加或减少信息准则选择正确模型的概率。仿真结果证实了我们在有限样本下的渐近结果。
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英文标题：
《Model Selection for Explosive Models》
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作者：
Yubo Tao and Jun Yu
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最新提交年份：
2017
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
This paper examines the limit properties of information criteria (such as AIC, BIC, HQIC) for distinguishing between the unit root model and the various kinds of explosive models. The explosive models include the local-to-unit-root model, the mildly explosive model and the regular explosive model. Initial conditions with different order of magnitude are considered. Both the OLS estimator and the indirect inference estimator are studied. It is found that BIC and HQIC, but not AIC, consistently select the unit root model when data come from the unit root model. When data come from the local-to-unit-root model, both BIC and HQIC select the wrong model with probability approaching 1 while AIC has a positive probability of selecting the right model in the limit. When data come from the regular explosive model or from the mildly explosive model in the form of $1+n^{\alpha }/n$ with $\alpha \in (0,1)$, all three information criteria consistently select the true model. Indirect inference estimation can increase or decrease the probability for information criteria to select the right model asymptotically relative to OLS, depending on the information criteria and the true model. Simulation results confirm our asymptotic results in finite sample.
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PDF链接：
https://arxiv.org/pdf/1703.02720
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