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Estimation of trend in state-space models: Asymptotic mean square error and rate of convergence

状态空间模型中的趋势估计:渐近均方误差与收敛速度

The focus of this paper is on trend estimation for a general state-space model Yt=μt+ɛt, where the dth difference of the trend {μt} is assumed to be i.i.d., and the error sequence {ɛt} is assumed to be a mean zero stationary process. A fairly precise asymptotic expression of the mean square error is derived for the estimator obtained by penalizing the dth order differences. Optimal rate of convergence is obtained, and it is shown to be “asymptotically equivalent” to a…

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Discrimination and Clustering for Multivariate Time Series

多元时间序列的判别与聚类

Minimum discrimination information provides a useful generalization of likelihood methodology for classification and clustering of multivariate time series. Discrimination between different classes of multivariate time series that can be characterized by differing covariance or spectral structures is of importance in applications occurring in the analysis of geophysical and medical time series data. For discrimination between such multivariate series, Kullback-Leibler…

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Forecasting With Dynamic Regression Models.

利用动态回归模型进行预测

A Primer on ARIMA Models. A Primer on Regression Models. Rational Distributed Lag Models. Building Dynamic Regression Models: Model Identification. Building Dynamic Regression Models: Model Checking, Reformulation, and Evaluation. Intervention Analysis. Intervention and Outlier Detection and Treatment. Estimation and Forecasting. Dynamic Regression Models in a Vector ARMA Framework. Appendices. References. Index.

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Adjustment of Provisional Mortality Series: The Dynamic Linear Model with Structured Measurement Errors

暂定死亡率序列的调整:含结构化测量误差的动态线性模型

The authors "consider the problem of adjusting provisional time series using a bivariate structural model with correlated measurement errors. Maximum likelihood estimators and a minimum mean squared error adjustment procedure are derived for a provisional and final series containing common trend and seasonal components. The model also includes measurement errors common to both series and errors that are specific to the provisional series. [The authors] illustrate the…

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Applied Regression and Analysis of Variance for Stationary Time Series

平稳时间序列的应用回归与方差分析

In the area of applied time series analysis a commonly occurring problem involves the detection and estimation of signals (regression functions) imbedded within a collection of independent identically distributed noise processes. A general linear model which represents each observed time series as the sum of a wide sense stationary error process and a vector of regression functions operated on by a matrix of time invariant observables includes as special cases many signal…

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