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稳定季节模式估计中最小二乘法的效率AI 解读

In this article we investigate the efficiency of least squares (l.s.) in estimating a stable pattern. A model is proposed for an economic time series, which, after filtering, is a suitable basis for our investigation. The covariance structure of the disturbances is assumed known and several possible generating processes for the disturbances are considered. We contrast the variances of the l.s. estimates with those from the best linear unbiased (b.l.u.) procedure for four…

连续时间分布滞后模型的离散近似AI 解读

A model is considered in which a covariance-stationary exogenous process is related to an endogenous process by an unrestricted, infinite, linear distributed lag. It is shown that when an underlying continuous time model is sampled at unit intervals to yield endogenous and exogenous discrete time processes, the discrete time processes are related by a discrete time equivalent of the underlying continuous model. The relationship between the underlying continuous lag…

相关随机效应分析：含两个随机分量的线性模型AI 解读

Linear regression models with two random components, one of which is time correlated, are analysed from a Bayesian viewpoint. The problem of making inferences about the parameters when the time correlated component is stationary is discussed. Necessary modifications needed for nonstationary and explosive models are indicated. The analysis is illustrated by a numerical example showing that the time series component of the data can exert a strong influence in determining the…

最小二乘回归中的一种新自相关检验AI 解读

The Durbin-Watson test on autocorrelation is based on the least squares residual vector. It is well known that the distribution of this vector depends upon the regression matrix which implies that tabulation of the test statistic's significance points is senseless. The best linear unbiased scalar test circumvents this difficulty and gives a test statistic whose distribution does not depend upon the regression matrix; it is an exact test. However, some objections can be made…

最小二乘回归中的序列相关检验（三）AI 解读

The paper considers a number of problems arising from the test of serial correlation based on the d statistic proposed earlier by the authors (Durbin & Watson, 1950, 1951). Methods of computing the exact distribution of d are investigated and the exact distribution is compared with six approximations to it for four sets of published data. It is found that approximations suggested by Theil and Nagar and by Hannan are too inaccurate for practical use but that the beta…

回归分析中扰动项的新估计量AI 解读

In this article, an alternative v for the vector û of least-squares residuals in the linear model is derived. It is best in the class of all linear unbiased estimators' of u having a certain fixed covariance matrix chosen a priori. Under the normality assumption, the distribution of the Von Neumann Ratio based on v is independent of the regression vectors, so that v is particularly useful for testing on serial correlation of the disturbances. It is pointed out that the…

使月度或季度序列与年度总量一致：基于二次最小化的方法AI 解读

This article considers the problem of adjusting monthly or quarterly time series to make them accord with independent annual totals or averages without introducing artificial discontinuities. A general approach and some specific procedures involving constrained minimization of a quadratic form in the differences between revised and unrevised series are proposed. Some computational advantages are noted. Attention is given to the relationships between the adjustment problem…

平稳多元时间序列的若干独立性检验AI 解读

Summary Let X(t)=(X1(t)X2(t)⋮XP(t)),t=⋯−1,0,1…, be a p-dimensional zero-mean stationary Gaussian time series possessing a spectral density matrix F(ω) = {fij(ω)}, i, j = 1, 2, …, p, satisfying some mild regularity conditions. Let F^(ωl), l=1, 2, … ,M, F^(ωl)={f^ij(ωl)} be suitably defined sample spectral density matrices for M values of ω, based on a record of length T ≫ M. We consider the following (null) hypotheses: H1: Xi(t), Xi(s) independent if i ≠ j, all s, t, H2:…

自回归移动平均误差回归模型中残差自相关的分布AI 解读

Summary In examining the adequacy of a statistical model an analysis of the residuals is often carried out; and for models involving a time series structure the serial correlations of the residuals are natural statistics to consider. In this paper it is shown that asymptotically the first s sample autocorrelations of the residuals, calculated from a least-squares fit of a regression model in which the errors follow a stationary autoregressive–moving average time series,…

基于累积和检验的变点推断AI 解读

The point of change in mean in a sequence of normal random variables can be estimated from a cumulative sum test scheme. The asymptotic distribution of this estimate and associated test statistics are derived and numerical results given. The relation to likelihood inference is emphasized. Asymptotic results are compared with empirical sequential results, and some practical implications are discussed.

相干性与群延迟的估计AI 解读

The usual estimation of coherence is known to be badly biased towards zero if over the band of frequencies used for its estimation the phase is changing rapidly, as in the case of large group delay. The usual asymptotic distribution theory for spectral estimates is of no value in this circumstance, since it does not involve the group delay. A new theory is used to obtain estimates of coherence and group delay, which is itself of considerable physical interest, and the…

自回归移动平均误差回归模型的最小二乘估计AI 解读

To treat the problem of correlated errors in regression, a model in which the errors follow a stationary autoregressive-moving average time series is suggested. Simultaneous least squares estimation of the regression and the time series parameters is discussed, and it is shown that asymptotically the estimates obtained in this manner possess normal distributions, whether or not the errors themselves are normally distributed. The estimates of the regression parameters are…

最小二乘回归中一种新的自相关检验AI 解读

The Durbin-Watson test on autocorrelation is based on the least squares residual vector. It is well known that the distribution of this vector depends upon the regression matrix which implies that tabulation of the test statistic's significance points is senseless. The best linear unbiased scalar test circumvents this difficulty and gives a test statistic whose distribution does not depend upon the regression matrix; it is an exact test. However, some objections can be made…

相关随机效应分析：含两个随机分量的线性模型AI 解读

Linear regression models with two random components, one of which is time correlated, are analysed from a Bayesian viewpoint. The problem of making inferences about the parameters when the time correlated component is stationary is discussed. Necessary modifications needed for nonstationary and explosive models are indicated. The analysis is illustrated by a numerical example showing that the time series component of the data can exert a strong influence in determining the…

最小二乘回归中的序列相关检验：第三篇AI 解读

The paper considers a number of problems arising from the test of serial correlation based on the d statistic proposed earlier by the authors (Durbin & Watson, 1950, 1951). Methods of computing the exact distribution of d are investigated and the exact distribution is compared with six approximations to it for four sets of published data. It is found that approximations suggested by Theil and Nagar and by Hannan are too inaccurate for practical use but that the beta…

1954 年与 1963 年大都市地区零售销售的决定因素AI 解读

This article presents several specifications of a retail sales model to explain the differential sales of retail goods and services in large Standard Metropolitan Statistical Areas in 1954 and 1963. Stepwise regression is employed and some hitherto unused regressors such as local government expenditures and taxes are introduced to compare different forms of the model specification. Tests on the stability of the relevant elasticities obtained in the model over time and on the…

平稳时间序列的应用回归与方差分析AI 解读

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…

ARIMA 时间序列模型中残差自相关的分布AI 解读

Many statistical models, and in particular autoregressive—moving average time series models, can be regarded as means of transforming the data to white noise, that is, to an uncorrected sequence of errors. If the parameters are known exactly, this random sequence can be computed directly from the observations; when this calculation is made with estimates substituted for the true parameter values, the resulting sequence is referred to as the “residuals,” which can be regarded…

1954年与1963年大型都市区零售销售的决定因素AI 解读

This article presents several specifications of a retail sales model to explain the differential sales of retail goods and services in large Standard Metropolitan Statistical Areas in 1954 and 1963. Stepwise regression is employed and some hitherto unused regressors such as local government expenditures and taxes are introduced to compare different forms of the model specification. Tests on the stability of the relevant elasticities obtained in the model over time and on the…

时间序列谱矩的估计AI 解读

The task of estimating moments of the spectrum of a stationary time series, rather than the more common problem of estimating the spectrum itself, is discussed. In particular, explicit formulae are deduced for the mean and variance of an estimator of the normalized standard deviation of the spectrum. Besides its theoretical significance, the necessity for estimating such a moment is of practical importance, for example, in the analysis of the velocity distributions of…

结构形式发生变化时的两阶段最小二乘估计AI 解读

1. IN THIS NOTE we consider the estimation of linear models when the coefficients of the structural form are not the same for all observations for which the model is postulated to be valid. An example of such a model is given in [3], where some structural relations have a piecewise linear form. Another example is the water melon market model of Suits [2] where there are two alternative harvest supply schedules. Also discussed here is the case where for one part of the sample…

分布滞后模型分析及其在消费函数估计中的应用AI 解读

SINCE KOYCK'S pioneering work, distributed lag models have come to play an important role in econometrics and much work has been done to develop methods for analyzing them-see e.g. Koyck [15], Klein [12], Solow [20], Fuller and Martin [5], Malinvaud [18], Hannan [9], Liviatan [17], Amemiya and Fuller [1], Zellner and Park [25], Thornber [21], Waud [23], Dhrymes [3], and Griliches [7]. In the present paper we present maximum likelihood and Bayesian estimation procedures for…

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.

对 Friedman 永久收入理论的直接检验AI 解读

After reviewing Friedman's time series model, this article presents a test of whether or not permanent consumption and transitory income are correlated. We conclude utilizing essentially the same data series and the same measure of permanent income as Friedman that a significant positive correlation exists between these variables as well as between permanent and transitory income.