Model Selection for Nested and Overlapping Nonlinear, Dynamic and Possibly Mis-Specified Models
Model Selection for Nested and Overlapping Nonlinear, Dynamic and Possibly Mis-Specified Models
复制标题
嵌套和重叠非线性、动态和可能错误指定模型的模型选择
DOI：
--
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
B. Rossi
中科院分区：
文献类型：
--
作者：
Massimiliano Marcellino;B. Rossi
关于模型比较的文献通常需要假设真实的条件分布对应于竞争模型之一的条件分布。这一强有力的假设已通过包含和基于可能性的模型比较的概念得到扩展。本文采用后一种方法，并开发了用于比较竞争非线性动态模型的测试，重点关注嵌套和重叠的情况。原假设是，根据某种接近程度，模型同样接近数据生成过程 (DGP)。另一种选择是使用一种更接近 DGP 的模型。模型可以正确指定，也可以不指定。它们的参数可以通过多种方法估计，包括（伪）最大似然法和普通最小二乘法。测试是对称的和定向的。它们在零值下的渐近分布要么是正态分布，要么是卡方分布的加权和，具体取决于竞争模型的嵌套特征。作为示例，讨论了嵌套 AR 模型以及具有 GARCH 误差和外生强迫变量的嵌套 ARMA 模型 (ARMAX-GARCH) 的比较。
The literature on model comparison often requires the assumption that the true conditional distribution corresponds to that of one of the competing models. This strong assumption has been extended by the notion of encompassing and in likelihood based model comparisons. This paper takes the latter approach and develops tests for the comparison of competing nonlinear dynamic models, focusing on the nested and overlaping cases. The null hypothesis is that the models are equally close to the data generating process (DGP), according to a certain measure of closeness. The alternative is that one model is closer to the DGP. The models can be correctly specified or not. Their parameters can be estimated by a variety of methods, including (pseudo) maximum likelihood and ordinary least squares. The tests are symmetric and directional. Their asymptotic distribution under the null is either normal or a weighted sum of chi-squared distributions, depending on the nesting characteristics of the competing models. The comparison of nested AR models, and of nested ARMA models with GARCH errors and exogenous forcing variables (ARMAX-GARCH) are discussed as examples.