Rodriguez Alejandro, Pino Gabriel, Herrera Rodrigo
Departamento de Ingeniería Industrial, Universidad de Talca, Curico, Chile.
Facultad de Economía y Negocios, Universidad de Talca, Talca, Chile.
J Appl Stat. 2020 Feb 25;48(3):471-497. doi: 10.1080/02664763.2020.1732885. eCollection 2021.
When prediction intervals are constructed using unobserved component models (UCM), problems can arise due to the possible existence of components that may or may not be conditionally heteroscedastic. Accurate coverage depends on correctly identifying the source of the heteroscedasticity. Different proposals for testing heteroscedasticity have been applied to UCM; however, in most cases, these procedures are unable to identify the heteroscedastic component correctly. The main issue is that test statistics are affected by the presence of serial correlation, causing the distribution of the statistic under conditional homoscedasticity to remain unknown. We propose a nonparametric statistic for testing heteroscedasticity based on the well-known Wilcoxon's rank statistic. We study the asymptotic validation of the statistic and examine bootstrap procedures for approximating its finite sample distribution. Simulation results show an improvement in the size of the homoscedasticity tests and a power that is clearly comparable with the best alternative in the literature. We also apply the test on real inflation data. Looking for the presence of a conditionally heteroscedastic effect on the error terms, we arrive at conclusions that almost all cases are different than those given by the alternative test statistics presented in the literature.
当使用未观测成分模型（UCM）构建预测区间时，由于可能存在条件异方差或同方差的成分，可能会出现问题。准确的覆盖率取决于正确识别异方差的来源。已将不同的异方差检验方法应用于UCM；然而，在大多数情况下，这些方法无法正确识别异方差成分。主要问题是检验统计量受序列相关性的影响，导致在条件同方差下统计量的分布仍然未知。我们基于著名的威尔科克森秩统计量提出了一种用于检验异方差的非参数统计量。我们研究了该统计量的渐近有效性，并考察了用于逼近其有限样本分布的自助法程序。模拟结果表明，同方差检验的规模有所改善，且功效与文献中最佳的替代方法明显相当。我们还将该检验应用于实际通胀数据。在寻找误差项上的条件异方差效应时，我们得出的结论是，几乎所有情况都与文献中给出的替代检验统计量的情况不同。
