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“解析”小波阈值化AI 解读

We introduce so-called analytic stationary wavelet transform thresholding where, using the discrete Hilbert transform, we create a complex-valued ‘analytic’ vector from which an amplitude vector is defined. Thresholding of a real-valued wavelet coefficient at some transform level is carried out according to the corresponding value in this amplitude vector; relevant statistical results follow from properties of the discrete Hilbert transform. Analytic stationary wavelet…

季节性持久过程周期图估计量的大样本性质AI 解读

Seasonally persistent models were first introduced by Anděl (1986) and Gray et al. (1989) to extend autoregressive moving‐average and fractionally differenced models and to encompass long‐memory quasi‐periodic behaviour. These models are, for certain ranges of parameters, stationary, and we prove here that the behaviour of the periodogram and other tapered estimators cannot be simply extended from the work of Künsch (1986) and Hurvich & Beltrao (1993) on long memory induced…