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曲线与周期图平滑AI 解读

Summary The difficulty in constructing smoothing formulae is to express quantitatively the type of smoothness one expects of the curve one is estimating. An argument is given in Sections 1 and 3 for formulating this “smoothness hypothesis” in terms of the properties of a population of curves of which the curve being estimated is a member. In equation (20) we obtain a solution for the matrix of optimum weighting coefficients in terms of certain “population moments” of the…

随机过程谱密度函数的估计AI 解读

Summary On the basis of an expected-mean-square-error criterion, the authors discuss the various hitherto proposed estimators of the spectral density function of a discrete-parameter process; they also introduce a new estimator. Any of these estimators depends on some parameter, and indications are given as to how this parameter should match those of the process in order to optimize the estimator. The alleged conflict between resolvability and statistical reliability is…

时间序列的谱分析AI 解读

Summary (i) A review has been made of spectral analysis and its relation with other branches of time-series analysis. A detailed account has been given of the methods available for estimating the spectral density, the band spectrum and the integrated spectrum; suggestions have also been made for confidence intervals for the latter two estimators. (ii) Emphasis has been laid throughout upon the difficulties which are met in practice and gaps in the theoretical structure have…

回归技术在季节校正与日历变动调整中的应用AI 解读

* The author wishes to acknowledge his indebtedness to Millard Hastay for suggesting the seasonal methods described below, and to Charlotte Boschan for intelligent assistance in all phases of the work.

自相关时间序列之间关系的回归分析AI 解读

Summary The properties of complete systems of linear regression equations, (in particular systems of the closed-loop and recursive type) are discussed in Part I, while least-square estimators and estimators of the Gauss-Markoff type are examined in Part II.

关于循环多元分布的一则札记AI 解读

In Anderson's (1941) paper on the distribution of serial correlation coefficients, Hotelling's suggestion of a circular definition of these coefficients appears. Since then this device has been used constantly to lighten the mathematical difficulties in serial correlation theory. There has, however, been no suggestion that the model would ever be a good approximation in practice—the reverse has always been suggested in fact. It is the purpose of the present note to point out…

线性自回归模型中的假设检验AI 解读

G. M. JENKINS; TESTS OF HYPOTHESES IN THE LINEAR AUTOREGRESSIVE MODEL: II. NULL DISTRIBUTIONS FOR HIGHER ORDER SCHEMES: NON-NULL DISTRIBUTIONS, Biometrika, Volu

具有正态残差的平稳时间序列谱分布函数的拟合优度检验AI 解读

A. M. WALKER; A GOODNESS OF FIT TEST FOR SPECTRAL DISTRIBUTION FUNCTIONS OF STATIONARY TIME SERIES WITH NORMAL RESIDUALS, Biometrika, Volume 43, Issue 3-4, 1 De

航空工程中的时间序列问题AI 解读

* Presented at the 114th Annual Meeting of the American Statistical Association at Montreal, September 11, 1954. This paper reviews some recent applications of random process theory to problems in aeronautical engineering. A number of random type disturbances that cause aeronautical problems are described and some of their effects on the airplane indicated. Particular attention is given to the effects of atmospheric turbulence in giving rise to airplane loads and structural…

为估计自回归参数增加短时间序列的有效长度AI 解读

Techniques of overcoming biases in serial correlation coefficients computed from short linear autoregressive time-series are considered. Two alternative estimates of autocorrelation coefficients are suggested as probable improvements over the usual estimates based on averages of observations made over a seasonal period. The alternative estimates are obtained, for example, from 12 yearly series, one for each month, and are: 1. an average of serial coefficients computed from…

去趋势马尔可夫序列最小二乘回归的数值研究AI 解读

Summary The variation in the standard error of the regression coefficient between two trend-reduced time series, constructed from Markoff series, is examined for various choices of the trend-reducing operator. Tables are given to facilitate computation, for the regression between trend-reduced time series which approximate to Markoff series in their local variational properties.

去趋势时间序列的最小二乘回归分析AI 解读

Summary The difficulties of obtaining a valid estimate of the standard error of a regression coefficient between two time series are discussed. It is shown how a preliminary trend-reducing operation on the series, using a moving average, makes it possible to obtain such a valid estimate. A method of analysis is described, along with considerations which affect the best choice of moving average for the purpose, which is applicable when the local variational properties of the…

系统性振荡检验的修订AI 解读

Summary This note suggests a revised test for the existence of systematic oscillation in the deviations of a time series from a fitted moving average. It is shown that the existing test may be misleading and simple alternative formulae are derived, though the test still remains subjective in the sense that the sampling distributions involved have not yet been derived.

马尔可夫自回归过程参数的置信区间AI 解读

Summary An investigation is made of two suggested methods by which confidence intervals might be indirectly obtained for the autocorrelation in a stationary first-order Markov series. The suggestions were to use in the one case the distribution of the mean of the disturbance terms, and in the other case the distribution of their serial correlation. It is shown that both methods give meaningful results if the observations do not diverge too greatly from the characteristics of…

基于破纪录次数的时间序列分布无关检验AI 解读

Summary Two simple statistics are proposed as distribution-free tests of the randomness of a series of observations. They are linear functions of the numbers of upper and lower records which occur in the series. They are uncorrelated and asymptotically normally distributed. One provides a consistent test against trend in the mean and the other a consistent test against trend in the variance. Power functions for the former test have been computed, and it is pointed out that…

随机过程频数分布的拟合优度AI 解读

The effect of the serial dependence of observations on the classical χ2 test is considered. For large correlations it is necessary to make the corrections to the mean and variance of χ2 given in this paper. The theory is illustrated with particular reference to the Poisson and normal Markoff processes. It is a pleasure to record my sincere thanks to Prof. M. S. Bartlett, under whose supervision thin work was done. To him I owe the suggestion of the problem, and his comments…

多变量自回归序列的拟合优度检验AI 解读

Summary The simplified method of derivation of Quenouille’s (1947) goodness of fit test for an autoregressive stationary series with discrete time, given by Bartlett and Diananda (1950), is extended in the present paper to the case of simultaneous autoregressive series, for which some interesting new features arise. The general solution is applied to a particular first-order process in two variables, the detailed correlational theory of which is being given elsewhere by…

多元平稳时间序列分析AI 解读

Summary After some preparatory work, the least square estimation equations are derived for a purely nondeterministic stationary multiple process (Th. 6). The asymptotic covariances of the parameter estimates are calculated for a normal process (Th. 9) and a test of fit derived (Th. 10). The testing of a sunspot model provides an illustration of the methods developed.

两种差分符号检验的功效AI 解读

SITUATIONS arise in which we are unable to make the assumptions necessary for the application of standard theory based on the normal distribution. Most of the distribution-free tests which have been proposed for such situations are based on statistics which are very easy to compute, and this ease of computation goes some way to compensate for any information, available in the sample, which may be ignored. Quite apart from such situations, it is interesting to investigate the…

系数随时间趋势变化的二阶自回归模型AI 解读

Summary It has been suggested that the departure of certain time series from a fitted second order autoregressive scheme is due to time-trending coefficients in the generating differential equation. If coefficients with linear time-trends are introduced into the scheme the correlogram of the resulting non-stationary series can, in special cases, be evaluated exactly in terms of Airy integrals and is found to be approximately of the form sin s/s where s is proportional to the…

线性自回归模型拟合优度检验的渐近功效函数性质AI 解读

Summary Quenouille (1947), and Bartlett and Diananda (1950), have given large sample goodness-of-fit tests of the hypothesis that a time series can be represented by a linear autoregressive scheme with independent residuals. Asymptotic power functions of these tests are derived for alternative hypotheses specified by linear autoregressive schemes of higher order with independent residuals, and of the same or higher order with residuals among which there exists dependence of…

利用连续有限差分估计标准误AI 解读

Summary Finite differences have been used to estimate random error in time series, the process being referred to as the variate-difference method (Kendall, 1948; Tintner, 1940). In this note an examination is made of the relative efficiencies of the various estimates of standard error obtained from mean differences and mean square differences (assuming a normal law), and to apply the results to the estimation of the standard error in the fitting of polynomials by means of…

区间的随机分割：第二部分AI 解读

Summary In a previous paper the theory of a test for the random distribution of events in time was considered. In the present paper a model is set up for a process in which events occur in time in a dependant manner. Using this model as an alternative hypothesis the asymptotic efficiency of the previously considered test is compared with that of a test proposed by M. S. Bartlett and it is found that the latter is considerably more efficient as well as being easier to use.

自回归模型中 Quenouille 检验的扩展AI 解读

M. S. Bartlett, P. H. Diananda; Extensions of Quenouille’s Test for Autoregressive Schemes, Journal of the Royal Statistical Society Series B: Statistical