Testing against smooth stochastic trends
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针对平滑随机趋势的检验
- 研究问题
- 如何区分确定性趋势与积分随机游走形成的平滑随机趋势，并在序列相关、季节变化或近单位根干扰下开展检验？
- 方法与思路
- 作者在未观测成分模型中构造趋势检验，推导渐近分布与临界值，并扩展到相关扰动、演变季节成分和界限检验。
- 材料陈述的贡献
- 摘要称，文章给出检验及多种扩展；总体比较支持基于创新构造、在非受限模型估计干扰参数的特定参数化检验。
- 阅读关注点
- 应核对积分随机游走的定义、白噪声与扩展设定，并区分原假设下估计参数的一致性结果和非受限估计的比较结论。
- 阅读边界
- 仅据所给 Crossref 摘要，无法判断各扩展的完整正则条件和具体功效；所谓最有效检验的结论不能外推到任意扰动过程。
原文摘要
Abstract A trend estimated from an unobserved components model tends to be smoother when it is modelled as an integrated random walk rather than a random walk with drift. This article derives a test of the null hypothesis that the trend is deterministic against the alternative that it is an integrated random walk. It is assumed that the other component in the model is normally distributed white noise. Critical values are tabulated, the asymptotic distribution is derived and the performance of the test is compared with the test against a trend specified as a random walk with drift. The test is extended to allow for serially correlated and evolving seasonal components. When there is a stationary process containing a single autoregressive unit root close to one, a bounds test can be applied. In the case of a first‐order autoregressive disturbance, it is shown that a consistent test can still be obtained by carrying out estimation of the nuisance parameters under the null hypothesis. The overall conclusion is that the most effective test against an integrated random walk is a parametric one based on the random walk plus drift test statistic, constructed from innovations, with the nuisance parameters estimated in the unrestricted model. Copyright © 2001 John Wiley & Sons, Ltd.