A test for second‐order stationarity of a time series based on the discrete Fourier transform

By Yogesh Kumar Dwivedi, S. Subba Rao. 2009

109 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics, Finance, Signal Processing

View Paper: https://www.semanticscholar.org/paper/8179d363fe976625eaaea4c41dd968ed485b66b1

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In Economics and Econometrics

1. Michael Vogt
2. Holger Dette

In Finance

1. Holger Dette
2. Michael Vogt
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In Signal Processing

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2. Holger Dette

Citations in the corpus

• Detecting gradual changes in locally stationary processes (2013, methodology): “ a local spectral density with a global version; see Paparoditis [22, 23], Dette et al. [8] and Preuˇ et al. [24] among others. A Portmanteau-type test has been constructed in Dwivedi & Subba Rao [10]; a Wavelet-based test can be found in von Sachs & Neumann [28]. To estimate the time point ”