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滞后窗估计量的高斯近似与谱密度同时置信带AI 解读

In this paper we consider the construction of simultaneous confidence bands for the spectral density of a stationary time series using a Gaussian approximation for classical lag-window spectral density estimators evaluated at the set of all positive Fourier frequencies. The Gaussian approximation opens up the possibility to verify asymptotic validity of a multiplier bootstrap procedure and, even further, to derive the corresponding rate of convergence. A small simulation…

多项式尾部噪声下的时间序列趋势估计AI 解读

For time series data observed at non-random and possibly non-equidistant time points, we estimate the trend function nonparametrically. Under the assumption of a bounded total variation of the function and low-order moment conditions on the errors we propose a nonlinear wavelet estimator which uses a Haar-type basis adapted to a possibly non-dyadic sample size. An appropriate thresholding scheme for sparse signals with an additive polynomial-tailed noise is first derived in…

非平稳计数时间序列的对数线性模型AI 解读

We propose a new model for nonstationary integer-valued time series which is particularly suitable for data with a strong trend. In contrast to popular Poisson-INGARCH models, but in line with classical GARCH models, we propose to pick the conditional distributions from nearly scale invariant families where the mean absolute value and the standard deviation are of the same order of magnitude. As an important prerequisite for applications in statistics, we prove absolute…