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基于贝叶斯方法的随机差分方程多期预测AI 解读

Given n observations on a system of linear stochastic difference equations with appropriate initial conditions, and given a prior density (possibly diffuse) of its parameters, this paper obtains the predictor of the time series k periods into the future with minimum mean squared error. Completely analytical solution is given for predictions from the first-order univariate system, and, in the general higher-order multivariate case, for k up to 5. econometric equations to…

用自回归模型近似移动平均过程的偏差AI 解读

A rather extensive empirical study of autoregressive approximations to first-order moving averages, and in particular their use in estimating the moving average coefficient, shows a significant bias to be present. This is of special importance now that autoregressive spectral estimators are becoming popular. Several conjectures are made about the cause of bias, and some procedures are developed to reduce this bias.

传递函数时间依赖性的若干检验AI 解读

In studies of linear open loop systems, the assumption of time invariance is often tacitly made. In this paper we exploit a convenient frequency-domain approach to furnish tests for the time dependence of a transfer function, which is the most crucial notion in the case of linear systems. An extension of Tukey's test for nonadditivity is given in § 4. The proposed tests are illustrated numerically with both simulated and real data.

群时延估计AI 解读

It is suggested that in estimating spectra and cross spectra for a pair of stationary series the estimation of the phase may be replaced by an estimate of the group delay, which is the derivative of phase with respect to frequency. An estimate is proposed and its asymptotic properties are investigated. The results are illustrated by simulation and by application to real data. The estimation of a group delay that is constant over a nondegenerate band is also discussed.

积分移动平均过程的样本自相关函数行为AI 解读

Little is known about the behaviour of the sample autocorrelation function when the generating stochastic process is nonstationary. In this note the behaviour of the sample autocorrelation function for a particular integrated moving average process is examined and the implications for model identification are discussed.

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…

高斯自回归移动平均模型的最大似然辨识AI 解读

Closed form representations of the gradients and an approximation to the Hessian are given for an asymptotic approximation to the log likelihood function of a multidimensional autoregressive moving average Gaussian process. Their use for the numerical maximization of the likelihood function is discussed. It is shown that the procedure described by Hannan (1969) for the estimation of the parameters of one-dimensional autoregressive moving average processes is equivalent to a…

从回归分析视角理解线性动态递归估计AI 解读

A large class of useful multivariate recursive time series models and estimation methods has appeared in the engineering literature. Despite the interest and utility which this recursive work has when viewed as an extension of regression analysis, little of it has reached statisticians working in regression. To overcome this we (a) present the relevant random-β regression theory as a natural extension of conventional fixed-β regression theory and (b) derive the optimal…

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.

重新考察平稳随机回归参数的估计AI 解读

This article reexamines the problem of estimation in repeated regression experiments wherein the regression parameters vary according to a stationary stochastic process with known covariance structure. Best linear unbiased estimators, more efficient than those recently proposed by Burnett and Guthrie, are derived.

动态扰动时间序列模型的残差相关与诊断检查AI 解读

In examining adequacy of fit of a statistical model the stochastic properties of the residuals are often studied. In particular, for an important class of time series models involving an exogenous or input variable and correlated errors or disturbances, Box and Jenkins [1] recommend an examination of the autocorrelations of the residuals and the cross correlations between the residuals and the independent variable. It is shown in this article that the residual auto- and…

聚合对自回归模型预测的影响AI 解读

The article shows that if the original variable follows a pth order autoregressive system then the non-overlapping moving sum follows a pth order autoregression with at most a pth order moving-average of an independent sequence regardless of the length of the summation. From such an aggregate model we derive the optimal predictor of the aggregate variable and show that it performs remarkably well compared to the optimal disaggregate predictor. The article contains both…

自相关误差下结构方程的小样本估计AI 解读

Many time series models have autocorrelated errors. A further problem may be that some of the right-hand variables are correlated with the error. Using Monte Carlo methods we investigated several estimators of such a model. We found that a transformation to correct the autocorrelation often improved matters, but that techniques to correct the other problems such as instrumental variables were usually ineffective. In many cases ordinary least squares had the smallest mean…

平稳随机回归参数估计的重新考察AI 解读

This article reexamines the problem of estimation in repeated regression experiments wherein the regression parameters vary according to a stationary stochastic process with known covariance structure. Best linear unbiased estimators, more efficient than those recently proposed by Burnett and Guthrie, are derived.

随机模型假设检验中卡方检验与似然比检验的小样本功效比较AI 解读

When applying the Markov model, it is often assumed the transition matrix is stationary and of order one. This article considers the problem of applying the transformed likelihood ratio statistic and the contingency statistic to testing the assumptions of a particular order and of stationarity when the assumptions are not true. A Monte Carlo study of the small sample power of both these test statistics shows that if the true alpha level is kept equal for the two tests they…

美国石油炼制行业的经济—线性规划模型AI 解读

The linking of statistically estimated relationships with an engineering linear programming model offers important potentials for simulation and forecasting models of industries. This article describes such a model of the U.S. petroleum refining industry. Econometric techniques are used to specify product demands, prices, and some technical adjustments. A linear programming specification of the production function, assuming cost minimization, determines crude oil input…

有限遍历马尔可夫链转移概率估计中的初始状态选择AI 解读

The properties of the maximum likelihood estimators for the transition probabilities in a two-state ergodic Markov chain depend upon the choice of the initial states. For example, the initial states may be suitably fixed in advance or may be observed from the equilibrium distribution of the chain. A large number of relatively short realizations are assumed available and the asymptotic variances are examined in some detail. The relevant asymptotic covariance matrices are…

Haitovsky, Y., Multicollinearity in Regression Analysis: Comment, this REVIEW, LI (Nov. 1969), 486-489. Hocking, R. R., and R. N. Leslie, Selection of the Best Subset in Regression Analysis, Technometrics, Vol. 9, No. 4 (Nov. 1967), 531-540. Kendall, M. G., A Course in Multivariate Analysis (London: Charles Griffin and Company Ltd., 1957). Kendall, M. G., and A. Stuart, The Advanced Theory of Statistics, 3 (London: Charles Griffin and Company Ltd., 1966). Lancaster, K.,…

时间序列中的异常值AI 解读

Summary Two models are considered for outliers and their effects in time series. Likelihood ratio and approximate likelihood ratio criteria are derived for these models and the power functions are compared with that of the approach generally applied in the past.

计量经济学：统计基础与应用AI 解读

1. Elementary Aspects of Multivariate Analysis.- 1.1 Preliminaries.- 1.2 Joint, Marginal, and Conditional Distributions.- 1.3 A Mathematical Digression.- 1.4 The Multivariate Normal Distribution.- 1.5 Correlation Coefficients and Related Topics.- 1.6 Estimators of the Mean Vector and Covariance Matrix and their Distribution.- 1.7 Tests of Significance.- 2. Applications of Multivariate Analysis.- 2.1 Canonical Correlations and Canonical Variables.- 2.2 Principal Components.-…

季度回归方程中四阶自相关的检验AI 解读

A test for fourth order autocorrelation in the error term of a regression equation estimated from quarterly data is described. The development draws on the finite sample results of Durbin and Watson and illustrates how their procedure for the first order case can be generalized. In the model y = X,B + u where X is a matrix of fixed regressors and u, = put-4 + Bt, an appropriate test statistic for Ho: p = 0 is the statistic d4 = {z- )2/z2 computed from the least squares…

宽平稳自回归序列观测均值的估计AI 解读

This study concerns the relative efficiency of the least-squares estimator of the mean of a covariance stationary sequence that has a constant mean and an autoregressive representation of order p. Our results augment those in [2]. The results in Section 1 include for any positive integer p the variance of the LSE, the BLUE in terms of autoregressive coefficients, the variance of the BLUE and the range of applications of Ylvisaker's theorem [7] regarding a lower bound on…

分布滞后模型中的季节变动AI 解读

The dependent variable in a distributed lag model frequently exhibits a distinct seasonal pattern which cannot be attributed to the seasonal behavior of the independent variable. This article illustrates the advantages of using the variable lag model to incorporate these seasonal influences directly into the distributed lag relationship.

切换回归估计的一种新方法AI 解读

In recent years much attention has been focussed on the problem of discontinuous shifts in regression regimes at unknown points in the data series. This article approaches this problem by assuming that nature chooses between regimes with probabilities λ and 1 — λ. This allows formulation of the appropriate likelihood function maximized with respect to the parameters in the regression equations and λ. The method is compared to another recent procedure in some sampling…