Testing Covariance Stationarity

In this paper, we show that the widely used stationarity tests such as the Kwiatkowski Phillips, Schmidt, and Shin (KPSS) test have power close to size in the presence of time-varying unconditional variance. We propose a new test as a complement of the existing tests. Monte Carlo experiments show that the proposed test possesses the following characteristics: (i) in the presence of unit root or a structural change in the mean, the proposed test is as powerful as the KPSS and other tests; (ii) in the presence of a changing variance, the traditional tests perform badly whereas the proposed test has high power comparing to the existing tests; (iii) the proposed test has the same size as traditional stationarity tests under the null hypothesis of stationarity. An application to daily observations of return on U.S. Dollar/Euro exchange rate reveals the existence of instability in the unconditional variance when the entire sample is considered, but stability is found in subsamples.     

Testing Covariance Stationarity

In this paper, we show that the widely used stationarity tests such as the Kwiatkowski Phillips, Schmidt, and Shin (KPSS) test have power close to size in the presence of time-varying unconditional variance. We propose a new test as a complement of the existing tests. Monte Carlo experiments show that the proposed test possesses the following characteristics: (i) in the presence of unit root or a structural change in the mean, the proposed test is as powerful as the KPSS and other tests; (ii) in the presence of a changing variance, the traditional tests perform badly whereas the proposed test has high power comparing to the existing tests; (iii) the proposed test has the same size as traditional stationarity tests under the null hypothesis of stationarity. An application to daily observations of return on U.S. Dollar/Euro exchange rate reveals the existence of instability in the unconditional variance when the entire sample is considered, but stability is found in subsamples.     

中、日、韩长期购买力平价的非线性检验——基于1994-2009年的经验分析

购买力平价理论是一种基本的汇率决定理论,主要是检验实际汇率是否稳定。以往的研究主要是在线性模型的框架下,应用ADF和PP检验考察购买力平价是否成立。尝试在非线性的研究框架下,基于ESTAR模型应用KPSS检验方法对中、日、韩三国的长期购买力平价进行检验。实证分析结果表明,基于非线性的KPSS检验方法发现日本的实际汇率为非平稳时间序列,而中国和韩国的实际汇率为平稳序列。这说明长期中日本的购买力平价不成立,而中国和韩国的购买力平价成立。     

基于分整特性视角的我国股市长记忆性识别

金融时间序列的长记忆性检验常采用标度分析法，但结果往往不令人满意。从分整特性的新视角，利用KPSS检验和LW检验对我国股市收益及其波动的记忆性特征进行了深入研究。研究结果表明，我国股市的波动序列中存在显著的长记忆性。而收益序列本身无明显的长记忆性。这与成熟股票市场有关长记忆性的研究结论基本一致．与新兴股票市场的研究结论有所不同。此项结论对股市的长期投资者具有重要的决策意义。     

The effects of additive outliers on the seasonal KPSS test: a Monte Carlo analysis

This article builds on the test proposed by Lyhagen [The seasonal KPSS statistic, Econom. Bull. 3 (2006), pp. 1–9] for seasonal time series and having the null hypothesis of level stationarity against the alternative of unit root behaviour at some or all of the zero and seasonal frequencies. This new test is qualified as seasonal-frequency Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test and it is not originally supported by a regression framework.

The purpose of this paper is twofold. Firstly, we propose a model-based regression method and provide a clear illustration of Lyhagen's test and we establish its asymptotic theory in the time domain. Secondly, we use the Monte Carlo method to study the finite-sample performance of the seasonal KPSS test in the presence of additive outliers. Our simulation analysis shows that this test is robust to the magnitude and the number of outliers and the statistical results obtained cast an overall good performance of the test finite-sample properties.     

Effect of neglected deterministic seasonality on unit root tests

Whenever deterministic seasonality is ignored, the distribution of the Dickey-Fuller test is shifted to the left, with lower dispersion at the same time. When accounting for serial correlation, the distortions become less predictable. A Monte Carlo study confirms that the (augmented) Dickey-Fuller test without seasonal dummies is oversized and has little power at the same time, due to the need of lag augmentation. The effect of neglecting seasonal deterministics on the KPSS test for stationarity depends on the way the long-run variance is estimated. This is a shorter version of a working paper containing additional experimental evidence and the proofs of the propositions. The working paper is available online under http://www.wiwi.uni-frankfurt.de/~deme/ends_urt.pdf.     

时间趋势平稳性检验的带宽选择及其影响

本文将基于最小化两类错误的概率选择带宽的思想引入KPSS检验。文章通过蒙特卡罗仿真实验,对基于最小化均方误差和最小化两类错误概率的KPSS检验的有限样本性质进行了比较;并对中国季度实际GDP对数序列的平稳性进行了检验。结果表明,基于最小化两类错误概率的检验比基于最小化均方误差的检验有更大的水平扭曲,但前者也有更大的检验势;并且在误差项自回归系数小于等于0.5的大多数情形下,基于最小化两类错误概率的检验有更好的有限样本性质;中国季度实际GDP对数序列是带漂移的单位根过程。