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**Spectral correction for locally stationary Shannon wavelet processes.**
*(English)*
Zbl 1282.62210

Summary: It is well-known that if a time series is not sampled at a fast enough rate to capture all the high frequencies then aliasing may occur. Aliasing is a distortion of the spectrum of a series which can cause severe problems for time series modelling and forecasting. The situation is more complex and more interesting for nonstationary series as aliasing can be intermittent. Recent work has shown that it is possible to test for the absence of aliasing in nonstationary time series and this article demonstrates that additional benefits can be obtained by modelling a series using a Shannon locally stationary wavelet (LSW) process.

We show that for Shannon LSW processes the effects of dyadic-sampling-induced aliasing can be reversed. We illustrate our method by simulations on Shannon LSW processes and also a time-varying autoregressive process where aliasing is detected. We present an analysis of a wind power time series and show that it can be adequately modelled by a Shannon LSW process, the absence of aliasing can not be inferred and we present a dealiased estimate of the series.

We show that for Shannon LSW processes the effects of dyadic-sampling-induced aliasing can be reversed. We illustrate our method by simulations on Shannon LSW processes and also a time-varying autoregressive process where aliasing is detected. We present an analysis of a wind power time series and show that it can be adequately modelled by a Shannon LSW process, the absence of aliasing can not be inferred and we present a dealiased estimate of the series.

### MSC:

62M15 | Inference from stochastic processes and spectral analysis |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

65C60 | Computational problems in statistics (MSC2010) |

62P12 | Applications of statistics to environmental and related topics |

### Software:

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\textit{I. A. Eckley} and \textit{G. P. Nason}, Electron. J. Stat. 8, No. 1, 184--200 (2014; Zbl 1282.62210)

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