每日简报

大定义域函数型时间序列谱密度的深度学习估计AI 解读

We derive an estimator of the spectral density of a functional time series that is the output of a multilayer perceptron neural network. The estimator is motivated by difficulties with the computation of existing spectral density estimators for time series of functions defined on very large grids that arise, for example, in climate compute models and medical scans. Existing estimators use autocovariance kernels represented as large $G \times G$ matrices, where $G$ is the…

稳健小波 NKK 周期图的渐近分布AI 解读

This paper investigates the asymptotic distribution of a wavelet-based NKK periodogram constructed from least absolute deviations (LAD) harmonic regression at a fixed resolution level. Using a wavelet representation of the underlying time series, we analyze the probabilistic structure of the resulting periodogram under long-range dependence. It is shown that, under suitable regularity conditions, the NKK periodogram converges in distribution to a nonstandard limit…

高维时间序列预测的稀疏 Tucker 分解与图正则化AI 解读

Existing methods of vector autoregressive model for multivariate time series analysis make use of low-rank matrix approximation or Tucker decomposition to reduce the dimension of the over-parameterization issue. In this paper, we propose a sparse Tucker decomposition method with graph regularization for high-dimensional vector autoregressive time series. By stacking the time-series transition matrices into a third-order tensor, the sparse Tucker decomposition is employed to…