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From nonstationarity to stationarity via $1/f$ noise: discrete Fourier transforms and sample mean asymptotics for testingFrom nonstationarity to stationarity via $1/f$ noise: discrete Fourier transforms and sample mean asymptotics for testing

Mohamedou Ould Haye · Anne Philippe首次提交 2026-05-27 · 修订 2026-05-27 · v1arXiv预印本

经由 1/f 噪声连接非平稳与平稳：离散傅里叶变换及样本均值检验渐近理论AI 解读

We study the asymptotic behaviour of different statistics for time series exhibiting long memory and nonstationarity. For processes with memory parameter $d\in(-1/2,3/2)$ , we derive the joint limiting distribution of discrete Fourier transforms at a fixed number of Fourier frequencies, with a unified normalization. The resulting limits are Gaussian with an explicit covariance structure. Particular attention is given to the boundary case $d=1/2$ , also known as $1/f$ noise. We…We study the asymptotic behaviour of different statistics for time series exhibiting long memory and nonstationarity. For processes with memory parameter $d\in(-1/2,3/2)$, we derive the joint limiting distribution of discrete Fourier transforms at a fixed number of Fourier frequencies, with a unified normalization. The resulting limits are Gaussian with an explicit covariance structure. Particular attention is given to the boundary case $d=1/2$, also known as $1/f$ noise. We…

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关联记录被引 0 次 ↗OpenAlex · 核验 2026-10-01

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From nonstationarity to stationarity via 1/f1/f1/f noise: discrete Fourier transforms and sample mean asymptotics for testingFrom nonstationarity to stationarity via $1/f$ noise: discrete Fourier transforms and sample mean asymptotics for testing

From nonstationarity to stationarity via $1/f$ noise: discrete Fourier transforms and sample mean asymptotics for testingFrom nonstationarity to stationarity via $1/f$ noise: discrete Fourier transforms and sample mean asymptotics for testing