A test for second-order stationarity of a time series based on the discrete Fourier transform
A test for second-order stationarity of a time series based on the discrete Fourier transform
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DOI：
10.1111/j.1467-9892.2010.00685.x
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发表时间：
2011-01-01
影响因子：
0.9
通讯作者：
Rao, Suhasini Subba
中科院分区：
文献类型：
--
作者：
Dwivedi, Yogesh;Rao, Suhasini Subba
本文考虑零均值离散时间序列，定义了它在正则频率下的离散傅里叶变换。可以证明DFT在正则频率处是渐近不相关的当且仅当时间序列是二阶平稳的。利用这一重要性质，我们构造了一个Portmanteau型检验统计量来检验时间序列的平稳性。结果表明，在零的平稳性，检验统计量近似卡方分布。为了检验检验统计量的功效，建立了局部平稳替代下的渐近分布。它被证明是一个广义的非中心卡方，其中的非中心性参数测量的偏离平稳性。该测试与模拟，它被证明具有良好的权力。
We consider a zero mean discrete time series, and define its discrete Fourier transform (DFT) at the canonical frequencies. It can be shown that the DFT is asymptotically uncorrelated at the canonical frequencies if and only if the time series is second-order stationary. Exploiting this important property, we construct a Portmanteau type test statistic for testing stationarity of the time series. It is shown that under the null of stationarity, the test statistic has approximately a chi-square distribution. To examine the power of the test statistic, the asymptotic distribution under the locally stationary alternative is established. It is shown to be a generalized non-central chi-square, where the non-centrality parameter measures the deviation from stationarity. The test is illustrated with simulations, where is it shown to have good power.