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标量时间序列频谱的指数模型AI 解读

SUMMARY Existing procedures for obtaining linear prediction formulae for time series may be placed in two categories. The first consists of methods which involve fitting parametric models of the autoregressive or autoregressive moving average type. The second involves the factorization of an estimated spectral density function; this is essentially a nonparametric procedure. The procedure suggested in this paper contains elements of both of the above. Formally, it involves…

时间序列预测的误差AI 解读

Parametric and nonparametric procedures for the prediction of a time series are discussed. In each case the increase in the mean squared error of prediction, over its minimum level, due to the use of estimated spectra is assessed. The fitting of simple parametric models as approximations is also discussed.

时间序列预测误差研究AI 解读

Parametric and nonparametric procedures for the prediction of a time series are discussed. In each case the increase in the mean squared error of prediction, over its minimum level, due to the use of estimated spectra is assessed. The fitting of simple parametric models as approximations is also discussed.

回归分析中的同时置信带AI 解读

Summary Simultaneous confidence intervals for linear combinations of parameters in a regression analysis are discussed, and a desirable property is described. Confidence intervals having this property are characterized and the Working–Hotelling band is discussed with reference to it. It is shown how this band may be sharpened to give exact confidence levels in linear and quadratic regression. Tables are given from which the confidence bands may be constructed.

随机缺失观测下的谱分析AI 解读

Summary Spectral analysis of data with randomly missing observations is considered. Conditions are found under which consistent estimation of the spectral density function of the observed process is possible. An estimate is proposed and the results of a simulation study of its first two moments are presented.