TESTING FOR TREND
TESTING FOR TREND
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趋势测试
DOI：
10.1017/s0266466608080055
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发表时间：
2007
影响因子：
0.8
通讯作者：
A. Harvey
中科院分区：
文献类型：
--
作者：
F. Busetti;A. Harvey
本文考察了用于评估时间序列模型是否需要斜率分量的各种检验。我们首先考虑了一阶差值均值的简单t检验，并且证明了它对随机非平稳斜坡的另一种假设和对纯粹确定的斜坡都具有很高的功效。可以对检验进行参数修改或非参数修改，以处理序列相关性。利用局部极限功率变量和有限样本蒙特卡罗结果，我们将t检验与Vogelang(1998，Economrica 66,123-148)的非参数检验以及修正的平稳性检验进行了比较。总体而言，t检验似乎是一个很好的选择，特别是如果它是通过将参数模型与数据进行拟合来实现的。当用样本量的平方根进行标准化时，如果斜率是随机的，则简单的t统计量具有极限分布，并且没有对序列相关性进行校正。第二作者感谢经济和社会研究理事会(ESRC)作为区域时间序列动态公共因素模型项目的一部分提供的支持，授予L138 25 1008。我们也衷心感谢意大利银行的支持。2005年6月在意大利奥尔比亚举行的时间序列前沿问题会议和2005年9月在德国海德堡举行的NSF/NBER时间序列会议上介绍了本文件的早期版本；我们感谢几位与会者提出了有益的意见。我们还感谢Peter Phillips、Robert Taylor、Jesse Gonzalo以及在葡萄牙法罗举行的单位根和协整测试会议上的其他一些参与者提出了有用的意见。我们感谢保罗·罗德里格斯和两位裁判的评论。
The paper examines various tests for assessing whether a time series model requires a slope component. We first consider the simple t-test on the mean of first differences and show that it achieves high power against the alternative hypothesis of a stochastic nonstationary slope and also against a purely deterministic slope. The test may be modified, parametrically or nonparametrically, to deal with serial correlation. Using both local limiting power arguments and finite-sample Monte Carlo results, we compare the t-test with the nonparametric tests of Vogelsang (1998, Econometrica 66, 123–148) and with a modified stationarity test. Overall the t-test seems a good choice, particularly if it is implemented by fitting a parametric model to the data. When standardized by the square root of the sample size, the simple t-statistic, with no correction for serial correlation, has a limiting distribution if the slope is stochastic. We investigate whether it is a viable test for the null hypothesis of a stochastic slope and conclude that its value may be limited by an inability to reject a small deterministic slope.The second author thanks the Economic and Social Research Council (ESRC) for support as part of a project on Dynamic Common Factor Models for Regional Time Series, grant L138 25 1008. Support from the Bank of Italy is also gratefully acknowledged. Earlier versions of this paper were presented at the meeting on Frontiers in Time Series held in Olbia, Italy, in June 2005 and at the NSF/NBER Time Series conference in Heidelberg, Germany, in September 2005; we are grateful to several participants for helpful comments. We also thank Peter Phillips, Robert Taylor, Jesus Gonzalo, and a number of other participants at the Unit Root and Co-integration Testing meeting in Faro, Portugal, for helpful comments. We are grateful to Paulo Rodrigues and two referees for their comments.