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基于累积和检验的变点推断
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.
1954 年与 1963 年大都市地区零售销售的决定因素
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…
结构形式发生变化时的两阶段最小二乘估计
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…
线性模型中斜率系数发生变化的检验
A locally most powerful test is developed for the hypothesis that a slope coefficient in a linear time series model is stable, against the alternative that the slope shifts exactly once somewhere in the series. Analysis of the procedure using artificial data indicates good power characteristics even when the ratio of the shift size to the error variance is moderate—especially if the shift does not occur very near either end of the series. Power also depends on the pattern of…
随机变量序列中变点位置的推断
Inference is considered about the point in a sequence of random variables at which the probability distribution changes. In particular, we examine a normal distribution with changing mean. The asymptotic distribution of the maximum likelihood estimate is derived and also the asymptotic distribution of the likelihood ratio statistic for testing hypotheses about the change-point. These asymptotic distributions are compared with some finite sample empirical distributions.
季度投资行为计量模型的预测表现
In this paper four alternative quarterly econometric models of investment behavior are compared with regard to predictive performance. Predictive performance may be assessed in two ways: (i) We compare prediction errors for a period of prediction with errors for a period of fit. (ii) We fit investment functions for both periods and test for structural change. These two procedures may be viewed as alternative tests of the hypothesis of structural change; the second is more…
二项变量序列中变点的统计推断
The problem of making inferences about the point in a sequence of zero-one variables at which the binomial parameter changes is considered. The asymptotic distribution of the maximum likelihood estimate of the change-point is derived in computable form using random walk- results. The asymptotic distributions of likelihood ratio statistics for testing hypothesis about the change-point are also obtained. Some exact numerical results for these asymptotic distributions are given…
非平稳时间序列的水平变化
Suppose that observations zsubt of a time series are available at equally spaced time intervals. The authors consider the problem of making inferences about a possible shift in level of the series associated with the occurrance of an event E at some particular time. For example, the observations might be of some economic indicator and one might suspect a change in level to occur in a particular interval because of a change in fiscal policy. Alternatively, zsubt could be the…
最小二乘法在计量经济学中的地位
IN A RECENT paper,' Frederick V. Waugh argues strongly for the use of ordinary least squares in simultaneous systems. His argument is not that least squares gives unbiased estimates of structural parameters2 but that they do (as consistent structural estimators do not) give unbiased estimates of the dependent variable in the regression equation given the values of the other variables and that this is what is needed for forecasting purposes. This note argues that Waugh's…
家庭形成率及其组成的变化
In the prediction of future household formation, it proves useful to separate movements caused by population changes from those caused by shifts in the occurrence rates of households among a given population. The varying rates of occurrence reflect the differential impacts of economic vairables and social change. This study indicates that until better data are available, forecasts of households will have to rely primarily upon judgment. This can be gained from an analysis of…
线性回归系统两种体制的假设检验
Several approaches are explored for testing the hypothesis that no switch has occurred in the true values of the parameters of a linear regression system. The distribution of the relevant likelihood ratio λ is analyzed on the basis of the empirical distribution resulting from some sampling experiments. The hypothesis that −2 log λ has the χ2 distribution with the appropriate degrees of freedom is rejected and an empirical table of percentage points is obtained. Finally some…
线性回归系统两种机制切换的假设检验
Several approaches are explored for testing the hypothesis that no switch has occurred in the true values of the parameters of a linear regression system. The distribution of the relevant likelihood ratio λ is analyzed on the basis of the empirical distribution resulting from some sampling experiments. The hypothesis that −2 log λ has the χ2 distribution with the appropriate degrees of freedom is rejected and an empirical table of percentage points is obtained. Finally some…
具有两个不同状态的线性回归系统参数估计
In attempting to estimate the parameters of a linear regression system obeying two separate regimes, it is necessary first to estimate the position of the point in time at which the switch from one regime to the other occurred. The suggested maximum likelihood estimating procedure is based upon a direct examination of the likelihood function. An asymptotic and a small-sample test are suggested for testing the hypothesis that no switch occurred against the single alternative…