TESTING FOR WHITE NOISE UNDER UNKNOWN DEPENDENCE AND ITS APPLICATIONS TO DIAGNOSTIC CHECKING FOR TIME SERIES MODELS
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未知依赖下的白噪声检验及时间序列模型诊断
- 研究问题
- 当白噪声无自相关但存在非线性依赖或条件异方差时，如何保证 Box–Pierce 类检验及时间序列残差诊断的有效性？
- 方法与思路
- 作者研究带一般权重的 Box–Pierce 统计量，让滞后截断数随样本量适当增长，并应用于 ARMA 与 FARIMA 模型诊断。
- 材料陈述的贡献
- 摘要称，适当增长的截断数使检验在未知弱依赖下保有渐近零分布，并容许模型误差非高斯且具有条件异方差。
- 阅读关注点
- 应核对弱依赖与矩条件、权重和截断数的增长限制，以及估计模型参数后残差检验的分布是否需调整。
- 阅读边界
- 解读限于所给 Crossref 摘要。摘要未给出截断增长率或完整依赖条件，不能将未知弱依赖下的结论推广至任意依赖。
原文摘要
Testing for white noise has been well studied in the literature of econometrics and statistics. For most of the proposed test statistics, such as the well-known Box–Pierce test statistic with fixed lag truncation number, the asymptotic null distributions are obtained under independent and identically distributed assumptions and may not be valid for dependent white noise. Because of recent popularity of conditional heteroskedastic models (e.g., generalized autoregressive conditional heteroskedastic [GARCH] models), which imply nonlinear dependence with zero autocorrelation, there is a need to understand the asymptotic properties of the existing test statistics under unknown dependence. In this paper, we show that the asymptotic null distribution of the Box–Pierce test statistic with general weights still holds under unknown weak dependence as long as the lag truncation number grows at an appropriate rate with increasing sample size. Further applications to diagnostic checking of the autoregressive moving average (ARMA) and fractional autoregressive integrated moving average (FARIMA) models with dependent white noise errors are also addressed. Our results go beyond earlier ones by allowing non-Gaussian and conditional heteroskedastic errors in the ARMA and FARIMA models and provide theoretical support for some empirical findings reported in the literature.