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Hermitian 正定矩阵曲线的内蕴小波回归AI 解读

Intrinsic wavelet transforms and wavelet estimation methods are introduced for curves in the non-Euclidean space of Hermitian positive definite matrices, with in mind the application to Fourier spectral estimation of multivariate stationary time series. The main focus is on intrinsic average-interpolation wavelet transforms in the space of positive definite matrices equipped with an affine-invariant Riemannian metric, and convergence rates of linear wavelet thresholding are…

局部平稳因子模型：识别与非参数估计AI 解读

In this paper we propose a new approximate factor model for large cross-section and time dimensions. Factor loadings are assumed to be smooth functions of time, which allows considering the model as locally stationary while permitting empirically observed time-varying second moments. Factor loadings are estimated by the eigenvectors of a nonparametrically estimated covariance matrix. As is well known in the stationary case, this principal components estimator is consistent…

非平稳时间序列的动态因子模型拟合AI 解读

Factor modelling of a large time series panel has widely proven useful to reduce its cross-sectional dimensionality. This is done by explaining common co-movements in the panel through the existence of a small number of common components, up to some idiosyncratic behaviour of each individual series. To capture serial correlation in the common components, a dynamic structure is used as in traditional (uni- or multivariate) time series analysis of second order structure, i.e.…

重复时间序列谱的混合效应模型与树结构小波估计AI 解读

This article develops a method for estimating the spectrum of a stationary process using time series traces recorded from experimental designs. Our procedure estimates the “common” log-spectrum and the variability over the traces (or subjects) using a mixed effects model. We combine spatially adaptive smoothing methods with recursive dyadic partitioning to construct a model for predicting subject-specific effects. The method is easy to implement and can handle large datasets…

演化小波谱的局部自适应估计AI 解读

We introduce a wavelet-based model of local stationarity. This model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time. A notion of time-varying wavelet spectrum is uniquely defined as a wavelet-type transform of the autocovariance function with respect to so-called autocorrelation wavelets. This leads to a natural representation of the autocovariance which is localized on…

多元非平稳时间序列的 SLEX 分析AI 解读

We develop a procedure for analyzing multivariate nonstationary time series using the SLEX library (smooth localized complex exponentials), which is a collection of bases, each basis consisting of waveforms that are orthogonal and time-localized versions of the Fourier complex exponentials. Under the SLEX framework, we build a family of multivariate models that can explicitly characterize the time-varying spectral and coherence properties. Every model has a spectral…

用于时变谱分析的平滑样条 ANOVAAI 解读

In this article we propose a smoothing spline ANOVA model (SS-ANOVA) to estimate and to make inference on the time-varying log-spectrum of a locally stationary process. The time-varying spectrum is assumed to be smooth in both time and frequency. This assumption essentially turns a time-frequency spectral estimation problem into a 2-dimensional surface estimation problem. A smooth localized complex exponential (SLEX) basis is used to calculate the initial periodograms, and a…

二元非平稳时间序列的自动统计分析AI 解读

We propose a new method for analyzing bivariate nonstationary time series. The proposed method is a statistical procedure that automatically segments the time series into approximately stationary blocks and selects the span to be used to obtain the smoothed estimates of the time-varying spectra and coherence. It is based on the smooth localized complex exponential (SLEX) transform, which forms a library of orthogonal complex-valued transforms that are simultaneously…

各向异性函数类中的小波阈值估计及演化谱自适应估计AI 解读

We derive minimax rates for estimation in anisotropic smoothness classes. These rates are attained by a coordinatewise thresholded wavelet estimator based on a tensor product basis with separate scale parameter for every dimension. It is shown that this basis is superior to its one-scale multiresolution analog, if different degrees of smoothness in different directions are present. As an important application we introduce a new adaptive waveletestimator of the time-dependent…