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利用零点估计平稳二元高斯过程的互谱AI 解读

Summary Under regularity conditions the cross-spectrum of a stationary, bivariate, Gaussian process, continuous in mean and with unit variance, may be estimated consistently as T → ∞ from the zeros in the interval [0, T] of its two components and the knowledge that the components have the same or opposite sign at time 0. The power spectra of the components may be estimated from the respective components' zeros alone. The estimates are asymptotically normal and unbiased.…

非平稳过程的谱概念AI 解读

Summary Following a brief general description of the attitude adopted here to statistical models and definitions, a study of the problem of defining a spectrum for non-stationary processes is made. The approach is to determine first what one would wish to use such a spectrum for, and then attempt to discover whether this is possible. By the nature of the case no conclusive answer is possible, but the tentative conclusion drawn is that it is not.

随机滞后与分项构成时间序列的参数及关系AI 解读

A model is constructed for three related time series: an inflow, a stock, and an outflow. The inflow and outflow time series are related via a truly stochastic distributed lag and the three time series are viewed as cumulations of a random number of units of randomly determined size. Among the interesting results are the serial correlations of the stock and outflow time series viewed singly and the cross and cross serial correlations between outflow in t and stock at t -1,…

p 依赖时间序列离散程度趋势检验中 Cox–Stuart 检验的渐近相对效率AI 解读

Cox and Stuart's tests (Cox & Stuart, 1955) are applied to test for trend in dispersion of a p-dependent time series. For a particular trend model the asymptotic relative efficiencies are obtained for the S1 and S2 tests relative to the teat based on the maximum likelihood estimate.

非平稳过程的预测AI 解读

Summary We consider the problem of linear least-squares prediction for a class of non-stationary processes which possess “evolutionary spectral representations”. It is shown that, under certain conditions, such processes admit moving-average representations in terms of time-dependent coefficients. This feature enables us to develop a close analogue of the Wiener–Kolmogorov approach to the corresponding problem for stationary processes.

有限样本蒙特卡洛研究：一个自回归示例AI 解读

In this paper the problem of choosing among point estimators on the basis of their small sample properties is discussed from the sampling point of view. The indeterminacy of most Monte Carlo studies is analysed and resolved within the framework of statistical decision theory. A first order autoregressive model is worked through in detail both for its own sake and to illustrate how a complete Monte Carlo study might be done.

有限样本Monte Carlo研究：自回归模型示例AI 解读

In this paper the problem of choosing among point estimators on the basis of their small sample properties is discussed from the sampling point of view. The indeterminacy of most Monte Carlo studies is analysed and resolved within the framework of statistical decision theory. A first order autoregressive model is worked through in detail both for its own sake and to illustrate how a complete Monte Carlo study might be done.

引入折扣权重的估计方法AI 解读

Summary In the estimation of the parameters in time series models arising in economic and business situations, it is often of value to introduce some method of discounting which produces updated estimators that give more weight to recent data than to that arising in the distant past. The simplest methods of introducing such discounting are to modify the traditional methods of estimation. Such modifications are discussed for the methods of moments, least squares and maximum…

平稳随机过程中的离散抽样与移动和AI 解读

Assume that an autoregression generates the basic data but that the observations are an equi-spaced sample of moving sums of the basic data for non-overlapping discrete intervals. Simple least squares estimates of the underlying autoregression are not consistent. It is shown that it is possible to estimate consistently the coefficients of the underlying autoregression based on the equi-spaced sample. These results are equivalent to showing how to interpolate a finite number…

扰动同时存在序列相关与同期相关时回归方程组的有效估计AI 解读

This paper considers the problem of obtaining efficient estimates for the parameters of a system of M regression equations. The disturbance terms of this system are assumed to be related by both serial and contemporaneous correlation. Under the further assumption that the serial correlation is a first order autoregressive process, the paper develops an estimator that is consistent and has the same asymptotic normal distribution as the Aitken estimator which assumes the…

数据修订与经济预测AI 解读

The paper determines whether the earliest published indication of changes in GNP provide information which is useful in the interpretation of economic trends or whether subsequent revisions reveal that the true movements were radically different from those initially reported. An analysis of the provisional and advance data indicated that the initial changes differed from the final changes but still approximated the true pattern of the movements. Some of the data revisions,…

回归分析中扰动估计的进一步讨论AI 解读

For the well-known general linear model Theil has recently developed the so-called best linear disturbance estimates with a covariance matrix equal to σ2 I. In this article we give a slightly different formulation of his problem which may give us some more insight in this estimation procedure. An important check on the computations of these estimates is given, as well as a comparison of these estimates with the commonly used least-squares estimates. For some special cases…

用于计量经济分析的数据季节调整AI 解读

An earlier paper [3] provides axioms for the seasonal adjustment of economic time series. Seasonally adjusted data should be minimum variance, unbiased, and linear in an appropriate sense. These axioms yield a unique method for seasonal adjustment. The seasonally adjusted data may be obtained by an application of ordinary least squares regression.1 The problem of seasonal adjustment of economic time series in [3] is not the same as the problem of seasonal adjustment of data…

回归分析中扰动估计的进一步讨论AI 解读

For the well-known general linear model Theil has recently developed the so-called best linear disturbance estimates with a covariance matrix equal to σ2 I. In this article we give a slightly different formulation of his problem which may give us some more insight in this estimation procedure. An important check on the computations of these estimates is given, as well as a comparison of these estimates with the commonly used least-squares estimates. For some special cases…

用于计量经济分析的数据季节调整AI 解读

An earlier paper [3] provides axioms for the seasonal adjustment of economic time series. Seasonally adjusted data should be minimum variance, unbiased, and linear in an appropriate sense. These axioms yield a unique method for seasonal adjustment. The seasonally adjusted data may be obtained by an application of ordinary least squares regression.1 The problem of seasonal adjustment of economic time series in [3] is not the same as the problem of seasonal adjustment of data…

从削波平稳时间序列估计协方差与谱密度函数AI 解读

Summary When estimating the covariance functions of a stationary time series from a digitalized record, adjustments to the estimates must be made to correct for the bias caused by digitalizing. In this paper we investigate a method which provides consistent estimates of the covariance and the spectral density functions, and discuss their asymptotic efficiencies.

滞后回归关系的估计AI 解读

The paper discusses a technique for estimating the matrices of coefficients, B(j), in a regression relation relating a vector time series, z(n), to lagged values, y(n—j), —p ≤ j ≤ q, of a second vector time series. The technique depends upon calculation of spectra and cross-spectra. Once these are computed the estimates B(j) are obtained successively without recalculation when an additional lag is introduced. When the residuals from the regression are generated by a linear…

指数分布变量的序列相关检验AI 解读

This paper considers the testing of serial correlation coefficients when the underlying distribution is negative exponential. The first-order serial correlation coefficient is shown to be an asymptotically most powerful test criterion for certain plausible alternative hypotheses. The mean of its distribution, assuming independence, is known and a bound and estimate for its variance are obtained. These are compared with sampling results of D. R. Cox. The distribution of the…

具有周期结构的时间序列AI 解读

Time series which are encountered in meteorology exhibit non-stationary behaviour. If a variable is observed at the same time each day, it appears to be stationary over a period of a few weeks, but there is a seasonal variation in structure (Monin, 1963). For example, the mean and spectral density are different in the summer and in the winter. The usual approach to this problem is to divide the year into parts and analyse the data separately for the same two or three months…

关于时间序列分析的若干讨论AI 解读

Techniques involving the direct study of the spectrum when analyzing time-series are reviewed, and comments made on such topics as estimating the spectral density function, testing for mixed spectra, eliminating a trend, cross-spectral analysis, and non-normality. Recent extensions of spectral analysis by the author to point and line processes are illustrated by reference to traffic data, including an estimate of the flow-density relation from a cross-spectral analysis.

部分调整与适应性预期模型误设造成的小样本偏差AI 解读

The “partial adjustment” and “adaptive expectations” models are simply special cases of a more general model. This fact has not been commonly recognized by investigators who have used one or the other of these two models in empirical economic research. An examination of the results of small sample experiments shows that the bias in the estimated regression coefficients and the estimated mean lag which occurs when either one of the models is fitted by least squares to data…

具有平稳误差的多元回归AI 解读

A practical computing technique is presented for the joint estimation of regression coefficients and the error spectrum in regression problems with stationary errors. In problems where unweighted least squares is not efficient, the procedure gives an estimate approaching the minimum variance linear unbiased estimate. Whether unweighted least squares is nearly efficient or not efficient, the procedure, in general, gives a much closer estimate of the covariance matrix of the…

修订后美国国民账户中的统计差额AI 解读

As is well known, the U. S. national accounts contain a “Statistical Discrepancy” which serves to reconcile estimates of GNP from the product and from the income side. While the Discrepancy is a measure only of overall consistency rather than of error, its magnitude and pattern over time do give some indication of the quality of the national accounts data. In the past, the Statistical Discrepancy has not always behaved as a quantitatively unimportant random error term—a…

修订后美国国民账户中的统计差额AI 解读

As is well known, the U. S. national accounts contain a “Statistical Discrepancy” which serves to reconcile estimates of GNP from the product and from the income side. While the Discrepancy is a measure only of overall consistency rather than of error, its magnitude and pattern over time do give some indication of the quality of the national accounts data. In the past, the Statistical Discrepancy has not always behaved as a quantitatively unimportant random error term—a…