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关于相依情形下稳健估计的进一步讨论AI 解读

Results of an earlier paper giving first order optimal robust $M$-estimators of a location parameter in certain dependent situations are extended to the case where the dependency can be modeled by a symmetric form of a $(2k + 1)$st order moving average scheme. It is also shown that the results can not be extended to finding second order optimal $M$-estimators. That is, no $M$-estimators can be optimal to the second order unless they explicitly adapt themselves to the assumed…

自回归拟合与周期图的关系及其应用AI 解读

The relation between fitting autoregression and periodogram is herein presented. More specifically, the asymptotic error covariance matrices of the estimates of the autoregressive parameters using Yule-Walker equations are expressed in terms of the periodogram. These expressions permit the immediate calculation of the error covariance matrices for various time series problems including the autoregressive spectral estimation and fitting autoregression to the data with…

实验设计对时间自相关的稳健性（一）：渐近理论与位置、线性回归的最优性AI 解读

A new asymptotic theory for studying the effect of dependence of the observations in experimental design for the linear model is developed. The uniform design is shown to be asymptotically optimal in a strong sense for estimating location and in a weaker sense for estimating the slope of a straight line regression. Numerical results supporting the asymptotics appear in a companion paper.

具有自回归移动平均误差的随机线性差分方程的极大似然估计AI 解读

A method is proposed for the estimation of a general class of scalar linear time series models. The model takes the form of a stochastic difference equation for the dependent variable with exogenous variable inputs, and the disturbances are autocorrelated through an autoregressive moving average process. In the present paper an asymptotically efficient yet computationally simple estimation procedure (in the time domain) is derived for this model. The resulting estimator is…

残差自相关时线性趋势最小二乘估计的效率AI 解读

first-order stationary Markoff process with zero mean and autocorrelation coefficient p, - 1 < p < 1, the greatest lower bound for the efficiency of the least-squares estimator of 8 (relative to the Gauss-Markoff estimator) over the interval 0;p < 1 is .753763. This compares with a greatest lower bound of .535898 for the relative efficiency of the Cochrane-Orcutt estimator of 38.

向量自回归模型的渐近预测均方误差AI 解读

This paper derives the asymptotic mean squared error of multistep prediction for the general vector autoregressive process. For one-step-ahead prediction the result is a surprisingly simple generalization of the result for the scalar autoregressive process. Results for multistep prediction are also derived for the regression model with autoregressive errors, where the set of exogenous variables follows a vector autoregressive process.

自回归移动平均系统识别的一则札记AI 解读

A discussion is given of the identification and parameterization of autoregressive-moving average systems in relation to the use of certain canonical forms.

利用样本自协方差估计自回归移动平均模型参数AI 解读

This paper generalizes the work of Godolphin (1977, 1978) for estimating parameters of the moving average model and of the general autoregressive moving average model by solving the approximate log likelihood equation of Walker (1964).

ARMA 模型残差自相关的有限样本分布AI 解读

We examine by simulation the finite sample properties of tests of model adequacy based on individual residual autocorrelations, and of portmanteau statistics based on several residual autocorrelations, for autoregressive-moving average models. Both nonseasonal and seasonal models are considered.

平稳时空过程分析：估计与预测AI 解读

The paper analyses a simultaneous linear model representing stationary spatial-temporal processes. For processes with unit spatial orders, a simple method to compute the likelihood function is developed. Unfortunately, this technique does not generalize to higher order processes. Alternative methods applicable to higher order processes are developed. Finally, it is shown how predictions can be made over time if the parameters are known.

平稳自回归移动平均模型的似然函数AI 解读

This paper examines the likelihood function of a stationary autoregressive-moving average model of order (p, q) and presents a method for its evaluation. Numerical results illustrating the computational efficiency of the method are given.

多元自回归移动平均模型的精确似然函数AI 解读

By making use of the properties of tensor products, this paper describes the derivation of an expression for the exact likelihood function of a stationary process generated by a vector autoregressive-moving average model using concentrated maximum likelihood techniques. Furthermore, in the process of deriving the likelihood function, a closed form expression for the covariance function of the process in terms of the coefficients of the model is derived.

时间序列中若干异常值问题的贝叶斯分析AI 解读

Two models, the aberrant innovation model and the aberrant observation model, are considered to characterize outliers in time series. The approach adopted here allows for a small probability α that any given observation is ‘bad’ and in this set-up the inference about the parameters of an autoregressive model is considered.

周期自回归的若干结果AI 解读

SUMMARY Several properties of a periodic autoregressive process {x8} are examined by considering a related stationary multivariate autoregressive process. The properties of interest include: the representation of x8 as an infinite linear combination of independent, periodically distributed random variables, constraints on the parameters which permit such a representation, the covariance and spectral properties of {x8}, and the asymptotic behaviour of cumulative sums of {x8}…

自回归模型拟合中最小 AIC 程序的贝叶斯扩展AI 解读

The proposal of simultaneous use of modified AIC statistics by Bhansali & Downham for the fitting of autoregressive models is reviewed and a Bayesian extension of the minimum AIC procedure is proposed. The practical utility of the procedure is demonstrated by numerical examples.

混合自回归移动平均过程精确似然的计算算法AI 解读

The likelihood function for an autoregressive-moving average process is obtained by transforming the process to obtain a band covariance matrix whose Cholesky decomposition can be readily computed. Refinements are given for pure autoregressive and multiplicative seasonal processes. Evidence is presented to show that this approach allows more efficient computation than other methods proposed in the literature.

时间序列模型适切性的检验AI 解读

The problem of testing the adequacy of an autoregressive-moving average time series model is considered. A new approach is proposed, and some Monte Carlo results on the finite sample size and power of the test procedures of this paper are reported. The test statistics discussed by Box & Pierce (1970) and Ljung & Box (1978) are also examined.

具有ARMA扰动的回归模型的最大似然估计AI 解读

The regression model with autoregressive-moving average disturbances may be cast in a form suitable for the application of Kalman filtering techniques. This enables the generalized least squares estimator to be calculated without evaluating and inverting the covariance matrix of the disturbances. The problem of forecasting future values of the dependent variable is also effectively solved when the Kalman filter technique is applied. Furthermore, the properties of the…

参数估计后 ARMA 时间序列模型中 R² 的渐近分布AI 解读

The properties of the estimator of the squared multiple correlation coefficient, R2, for an autoregressive-moving average process are considered. It is shown that the estimator has an asymptotic distribution which is normal with mean .R2 and variance obtainable from the autocorrelations of the process.

时间序列模型设定综合检验的若干功效研究AI 解读

In this note we present simulation evidence on the power of a portmanteau statistic used to detect time series model misspecification. This is related to the loss in forecasting accuracy resulting from use of the incorrectly specified model. Our conclusion is that the statistic achieves a high level of success only when sample size is large.

已知方差的若干多元正态模型中相关系数的简易最优渐近正态估计AI 解读

It is well-known that in certain multivariate normal models with known variances, maximum likelihood estimation of correlations is arithmetically cumbersome. For certain of these models, a relatively simple estimation technique based on the sufficient statistics is given and shown to be best asymptotically normal. The procedure uses the fact that many of the likelihood equations for these models are essentially cubic equations. A consistent, explicit solution for the…

线性回归模型中随机游走系数存在性的精确检验AI 解读

Exact tests of the hypothesis that the mean vector of an observed T-variate random variable follows a conventional fixed-coefficient linear model, against the alternative that the regression parameters vary according to a first-order Markov process, are derived. Power functions of the tests are investigated in order to provide means of choosing a test.

若干已知方差多元正态模型中相关系数的简便最优渐近正态估计AI 解读

It is well-known that in certain multivariate normal models with known variances, maximum likelihood estimation of correlations is arithmetically cumbersome. For certain of these models, a relatively simple estimation technique based on the sufficient statistics is given and shown to be best asymptotically normal. The procedure uses the fact that many of the likelihood equations for these models are essentially cubic equations. A consistent, explicit solution for the…

时间序列分解的若干考察AI 解读

Suppose that an observable Gaussian time series Z1 can be written as the sum of an unobservable signal component Tt and a white noise component et. This paper proposes a procedure to estimate the Tt component uniquely by maximizing the variance of et with respect to a known model for Zt. Properties of this procedure are discussed and a comparison is made with a number of smoothing and filtering procedures commonly used in practice.