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Apparent correlation between independent series of autocorrelated observations

相互独立的自相关观测序列之间的表观相关

GILBERT WALKER, C.S.I., F.R.S., Sc.D.; Apparent correlation between independent series of autocorrelated observations, Biometrika, Volume 37, Issue 1-2, 1 June

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Note on Some Errors in “The Evidence of Periodicity in Short Time Series”

关于《短时间序列中的周期性证据》若干错误的说明

Several fundamental errors are in Truman Kelley's “The Evidence of Periodicity in Time Series.” These involve a confusion of numbers of observations and degrees of freedom, the interpretation of probabilities obtained in tests of hypotheses and the appropriateness of periodigram analysis for detecting the existence of periodicity in time series.

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By-Product Data and Forecasting in Unemployment Insurance

失业保险业务附带数据与预测

The unemployment insurance program has been operating in this country since the beginning of 1938. There have been many growing pains during these first eleven years. The operating problems involved in setting up this vast program have left little time thus far for careful consideration of the statistical data that are automatically produced in the course of its operations. These data, now and in the future, can be a fruitful source of information on changes in economic…

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A Sampling Study of the Merits of Auto-Regressive and Reduced form Transformations in Regression Analysis

回归分析中自回归变换与简约式变换的抽样研究

This paper is concerned with some aspects of regression analysis when the error terms are autocorrelated and there exists more than one relationship between the variables. In particular, we investigate the merits of autoregressive transformations and the reduced form transformation in dealing with these complications. An important result is that, unless it is possible to specify something about the intercorrelation of the error terms in a set of relations and to choose…

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By-Product Data and Forecasting in Unemployment Insurance

失业保险运行附带数据及其预测用途

The unemployment insurance program has been operating in this country since the beginning of 1938. There have been many growing pains during these first eleven years. The operating problems involved in setting up this vast program have left little time thus far for careful consideration of the statistical data that are automatically produced in the course of its operations. These data, now and in the future, can be a fruitful source of information on changes in economic…

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Application of Least Squares Regression to Relationships Containing Auto-Correlated Error Terms

含自相关误差关系中的最小二乘回归应用

We point out that autocorrelated error terms require modification of the usual methods of estimation and prediction; and we present evidence showing that the error terms involved in most current formulations of economic relations are highly positively autocorrelated. In doing this we demonstrate that when estimates of autoregressive properties of error terms are based on calculated residuals there is a large bias towards randomness. We demonstrate how much efficiency may be…

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Determination of Linear Relations between Systematic Parts of Variables with Errors of Observation the Variances of Which Are Unknown

观测误差方差未知时变量系统部分间线性关系的确定

Given a sufficient number of instrumental variables significantly correlated with the\ninvestigational variables, consistent estimates of the coefficients of the linear relations can be determined (if they exist), without knowledge of the disturbance variances. The estimates are discussed from the viewpoint of probability convergence. In the case of two investigational and one instrumental variable, all three variables distributed on the normal surface, the distribution of…

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Bank Reserves and Business Fluctuations

银行准备金与经济波动

The belief that severe business fluctuations are caused primarily by the operations of banks, through their influence on the quantity of the circulating medium, was widely held during the nineteenth century and the first three decades of the twentieth. During the latter part of this period variations in bank reserves were believed to be the chief causal factor underneath changes in the circulating medium furnished by the banks. This paper describes a study of factual data…

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A Note on the Statistical Estimation of Supply and Demand Relations from Time Series

关于从时间序列统计估计供需关系的札记

IN A discussion in this Journal of the estimation from time series of economic relations such as demand and supply equations, G. Tintner developed a technique based on multivariate methods of statistical analysis, the economic relations being identified with the linear relations existing (within the limits of observational error) among the economic variables considered. In the present note a more precise analysis of the same type is adopted in which some of the limitations…

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SOME THEOREMS ON TIME SERIES II. THE SIGNIFICANCE OF THE SERIAL CORRELATION COEFFICIENT

时间序列若干定理(二):序列相关系数的显著性

P. A. P. MORAN; SOME THEOREMS ON TIME SERIES II. THE SIGNIFICANCE OF THE SERIAL CORRELATION COEFFICIENT*, Biometrika, Volume 35, Issue 3-4, 1 December 1948, Pag

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Use of Variance Components in the Analysis of Hog Prices in Two Markets

两个市场生猪价格分析中的方差分量应用

This paper discusses various methods of analyzing the ratios of the daily hog prices at Cincinnati and Louisville and compares the results obtained with those previously given for the differences between the two price series. The data consisted of the prices for each of two weight classes on each the five complete market days of the week (Monday through Friday) averaged for each month throughout the period 1937-1941. Price ratios were used because of the high correlation…

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A Note on a Maximum-Likelihood Estimate

关于一种最大似然估计的札记

An estimate of y obtained by applying the method of maximum likelihood under the assumption that ut is normally distributed is consistent and asymptotically normally distributed. The asymptotic standard deviation is given in this note. Although Kendall considers many estimates of the period in his publication, he does not use the maximum-likelihood estimate although it has desirable properties in large samples that several of the other estimates do not have.4 It is…

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The Use of Econometric Models as a Guide to Economic Policy

以计量经济模型指导经济政策

IT IS desirable to provide tools of analysis suited for public economic policy that are, as much as possible, independent of the personal judgments of a particular investigator. Econometric models are put forth in this scientific spirit, because these models, if fully developed and properly used, eventually should lead all investigators to the same conclusions, independent of their personal whims. The usual experience in the field of economic policy is that there are about…

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The Oscillatory Properties of the Moving Average

移动平均的振荡性质

Summary The process of eliminating trend from a time series by means of the method of moving averages is shown to be extremely dangerous if the series is being examined for oscillatory movements. It is shown that the “trend free” moving average difference series formed by the difference between the terms of the original series and the moving average is always liable to be oscillatory whether or not the original series contains oscillatory components. The expression for the…

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Measuring and Forecasting Consumption

消费的测量与预测

During the past decade, under the stimulus of changed economic conditions and changed attitudes toward policy formation, real progress has been made in the measurement of consumption in the United States. Concepts have been clarified considerably, techniques for gathering information have been improved, some information has been collected, and a certain amount of lay as well as professional support has been developed for further use of public funds to measure consumption.…

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Measuring and Forecasting Consumption

消费的测量与预测

During the past decade, under the stimulus of changed economic conditions and changed attitudes toward policy formation, real progress has been made in the measurement of consumption in the United States. Concepts have been clarified considerably, techniques for gathering information have been improved, some information has been collected, and a certain amount of lay as well as professional support has been developed for further use of public funds to measure consumption.…

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The Variate Difference Method: A Reply

变量差分法:回应

(1) MR. HAAVELMO' contends that the variate difference method is not applicable to certain dynamic economic schemes, as, e.g., the cobweb theorem. It never has been claimed that this is the case, and the author has pointed out very carefully in his monograph2 that the variate difference method deals only with superimposed random variation. A more extensive discussion of the general problem of the role of errors in economics is to be found in a short article published in the…

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The Problem of Assigning a Length to the Cycle to be Found in a Simple Moving Average and in a Double Moving Average of Chance Data

随机数据经简单与双重移动平均后出现的周期长度判定问题

STATISTICIANS are familiar with the moving average. For example, when monthly prices are given, it may be desirable to eliminate the seasonal variation. The average of the monthly prices for a calendar year may be found, then the average of the prices from the February of this year to the January of the next, then from March to February, and so on. Each average thus formed involves just once each of the twelve months; and such averaging would seem a good method for…

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The Inadequacy of Testing Dynamic Theory by Comparing Theoretical Solutions and Observed Cycles

通过比较理论解与观测周期检验动态理论的不足

IN MODERN business-cycle research the following proceeding is being commonly used: First, a mathematical model (a determinate dynamic system) is set up, as an attempt to describe approximately the interconnections between a set of economic variables, their time derivatives, lagged values, and so on, in terms of strict functional relations. By some statistical procedure the constants in the system are estimated from the corresponding observed time series. Then the system is…

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On the Bartels Technique for Time-Series Analysis, and its Relation to the Analysis of Variance

Bartels 时间序列分析技术及其与方差分析的关系

IT HAS long been recognized that there is difficulty in applying the usual statistical techniques when there is correlation between successive items in any given sample. This trouble arises in many different fields: in economic time series the index number for any one day, month, or year is dependent on that of the preceding time unit. In sociology the number of strikes in progress at any one time is dependent on the number at some immediately preceding time. In agricultural…

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The Analysis of Economic Time Series

经济时间序列分析

T HE PROBLEM of the analysis of economic time series has occupied the attention of a great number of economists, mathematicians and statisticians, since the time when a considerable amount of statistical data became available in this field. It is probably one of the most unfortunate circumstances for our science that most economic data come in the shape of time series. Hence they cannot easily be dealt with by the ordinary statistical methods which have proven useful in…

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The Summation of Random Causes as the Source of Cyclic Processes

随机原因的叠加作为周期过程的来源

ALMOST ALL of the phenomena of economic life, like many other processes, social, meteorological, and others, occur in sequences of rising and falling movements, like waves. Just as waves following each other on the sea do not repeat each other perfectly, so economic cycles never repeat earlier ones exactly either in duration or in amplitude. Nevertheless, in both cases, it is almost always possible to detect, even in the multitude of individual peculiarities of the…

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