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连续时间局部平稳小波过程AI 解读

Abstract This article introduces the class of continuous-time locally stationary wavelet processes. Continuous-time models enable us to properly provide scale-based time series models for irregularly spaced observations for the first time, while also permitting a spectral representation of the process over a continuous range of scales. We derive results for both the theoretical setting, where we assume access to the entire process sample path, and a more practical one, which…

局部平稳小波时间序列中无混叠或局部白噪声的检验AI 解读

Aliasing is often overlooked in time series analysis but can seriously distort the spectrum, the autocovariance and their estimates.We show that dyadic subsampling of a locally stationary wavelet process, which can cause aliasing, results in a process that is the sum of asymptotic white noise and another locally stationary wavelet process with a modified spectrum.We develop a test for the absence of aliasing in a locally stationary wavelet series at a fixed location, and…