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ARMA 过程阶数的估计AI 解读

Under general conditions strong consistency of certain estimates of the maximum lags of an autoregressive moving average process is established. A theorem on weak consistency is also proved and in certain cases where consistency does not hold the probability of over-estimation of a maximum lag is evaluated.

最小二乘回归中序列相关的局部稳健检验AI 解读

Kariya and Eaton and Kariya studied a robustness property of the usual tests for serial correlation against departure from normality. When the results were applied to a regression model $y = X \beta + u(X: nxk),$ it was assumed that the column space of $X$ is spanned by some $k$ latent vectors of the covariance matrix of error term $u.$ In this paper we delete this assumption and in a much broader class of distributions derive a locally best invariant test for a one-sided…

月度时间序列中的日历效应：谱分析与图形检测AI 解读

Many time series, particularly national business and economic series, which are reported monthly and represent a total of the series for each month, contain calendar effects due to changing month length, weekly periodicities, and holidays. It is important to detect and remove this spurious calendar variation to allow a better appreciation of the variation in the series due to important factors. This article discusses detection. Two sets of diagnostic methods for detecting…

多变量 Portmanteau 综合检验统计量AI 解读

Box and Pierce have derived a goodness-of-fit test, the portmanteau test, for univariate autoregressive moving-average (ARMA) time series models. This test is here extended to multivariate ARMA models; the test statistic may be conveniently expressed as a function of the covariances between the residuals of the fitted model. A modified form of the statistic designed to have superior properties in small samples is derived, and the two forms of the statistic are compared via…

生长曲线技术在时间序列数据中的应用AI 解读

Techniques well established for the analysis of growth and dose response curves should provide useful tools for the analysis of time series data. After transforming the data to discrete Fourier transform coefficients, rather than to polynomial coefficients, as characterizes most growth curve techniques, further analysis is essentially the same. The circadian rhythm example reported by Ware and Bowden (1977) is reanalyzed, resulting in substantial reduction in width of…

生长曲线技术在时间序列数据中的应用AI 解读

Techniques well established for the analysis of growth and dose response curves should provide useful tools for the analysis of time series data. After transforming the data to discrete Fourier transform coefficients, rather than to polynomial coefficients, as characterizes most growth curve techniques, further analysis is essentially the same. The circadian rhythm example reported by Ware and Bowden (1977) is reanalyzed, resulting in substantial reduction in width of…

非线性模型中政策效应不确定性的估计AI 解读

asymptotic variances of multipliers for nonlinear models. It is used to estimate the uncertainty of the results of eight policy experiments for a particular model. ALTHOUGH MACROECONOMETRIC MOI)ELS are widely used to analyze the effects of alternative government actions on the economy, estimates of the uncertainty of these effects are rarely, if ever, presented. This is, of course, not surprising, since most macroeconometric models are nonlinear. Unlike for linear models,…

理性预期假说的检验AI 解读

This paper develops a test of the rational expectations hypothesis advanced by Muth [18]. The framework considered here allows for multiperiod expectations of several endogenous variables, with or without lagged exogenous variables. In conventional (linear) models, the hypothesis implies that the expectations are linear in certain relevant variables, and restricts the coefficients of these variables to be certain functions of the parameters in the imbedding model. The test…

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针对自相关正态备择的随机性非参数检验AI 解读

Locally most powerful rank tests of randomness against autocorrelated normal alternatives are derived. In particular, autoregressive and moving average alternatives are considered. The distribution of the statistic under the hypothesis of randomness is shown to be asymptotically normal. The small sample power of the test procedure is compared with that of two other procedures by the Monte Carlo Method.

傅里叶级数回归残差偏序列相关系数的近似分布AI 解读

Approximations are found to the joint distributions of noncircular and circular partial serial correlation coefficients calculated from residuals from regression on Fourier series. Results for coefficients calculated from deviations from the true mean and from the sample mean are obtained as special cases. It is shown that when the observations are independent the partial coefficients are approximately independently distributed in beta distributions that are the same for all…

充分估计量密度的近似方法AI 解读

A simple method of obtaining asymptotic expansions for the densities of sufficient estimators is described. It is an extension of the one developed by Barndorff-Nielsen & Cox (1979) for exponential families. A series expansion in powers of n−1 is derived of which the first term has an error of order n−1 which can effectively be reduced to n− / by renormalization.The results obtained are similar to those given by Daniels's (1954) saddlepoint method but the derivations are…

拟合自回归移动平均模型的设定检验AI 解读

This paper provides an extension of the application of score, or Lagrangian multiplier, tests to diagnostic checking of ARMA, autoregressive-moving average, models. The score test procedure for testing the null hypothesis of an ARMA( p,q ) process against certain ARMA ( p⊞r, q⊞s ) alternatives is considered and shown to be of the form of a pure significance test.

使用估计参数的多元自回归模型预测误差之渐近性质AI 解读

Summary In this paper we consider the asymptotic properties of the prediction errors for the multivariate autoregressive model when estimated coefficient parameters are used. Formulae for the asymptotic covariance matrix of the prediction errors for arbitrary lead times using estimated parameters are derived.

门限自回归、极限环与周期性数据AI 解读

Summary The notion of a limit cycle, which can only exist in a non-linear system, plays the key role in the modelling of cyclical data. We have shown that the class of threshold autoregressive models is general enough to capture this notion, a definition of which in discrete time is proposed. The threshold value has an interesting interpretation. Simulation results are presented which demonstrate that this new class of models exhibits some well-known features of non-linear…

线性回归模型中最小二乘估计量的强相合性AI 解读

For the linear regression model $y = X \beta + u$ with stochastic regressor matrix, strong consistency of the least squares estimator of $\beta$ is proved in the case of martingale difference errors and predetermined regressors and for the case where errors and regressors are orthogonal up to the second order. The results obtained are applied to parameter estimation in autoregressive processes, leading to strong consistency if the errors are quasi-independent up to the…

基于 ARMA 模型的递归估计AI 解读

A recursive estimate of the stochastic structure of a stationary time series is constructed based on the assumption that the true structure is ARMA, i.e., has a rational spectrum. The estimate is recursive in the sense that each successive estimate is obtained from the previous one by a relatively simple adjustment, that could be effected in a "real time" situation. The procedure is basically that of updating a regression when all variates involved are constructed from…

非线性平滑器的若干理论AI 解读

In recent years J. W. Tukey has introduced several algorithms for nonlinear smoothing of time series, but theoretical development has been slow owing to the extreme difficulty of obtaining analytical results even in the simplest cases. We present here some desiderata for smoothers generally, and give a framework within which some detailed comparisons between different smoothers can be made.

广告与总消费：Granger 因果关系分析AI 解读

This paper is concerned with testing for causation, using the Granger definition, in a bivariate time-series context. It is argued that a sound and natural approach to such tests must rely primarily on the out-of-sample forecasting performance of models relating the original (non-prewhitened) series of interest. A specific technique of this sort is presented and employed to investigate the relation between aggregate advertising and aggregate consumption spending. The null…

ARMA 误差对回归系数检验的影响：对 Vinod 文章的评论与扩展AI 解读

The problem that dependent disturbances may reverse the conclusions of t or F tests of the significance of the coefficients in least squares regression has been investigated by Vinod (1976). In this comment, imperfections in Vinod's article are indicated and improved results for a more general test are presented. Bounds on the critical values of the test of a set of linear constraints, including the simple significance test, are derived and calculated for disturbances…

单整 ARMA 过程样本自相关的渐近分布AI 解读

The behavior of the sample autocorrelation function, r(k), for an integrated autoregressive moving average time series is examined. The nonnormal asymptotic distribution of r(k) is characterized as a function of lag k and the parameters of the process. The validity of the approximation in moderate-sized samples is examined.

时间序列周期性的检验AI 解读

A one-parameter family of tests for periodicity in a time series is proposed that contains Fisher's test as a special case. Some tests in this family have substantially larger power than Fisher's test against many alternatives, yet retain comparable power against those alternatives for which Fisher's test is optimal. A Monte Carlo power study establishes this and also provides a basis for the selection of a test from this family. Critical values are obtained by using a…

改进多项式滞后对任意分布滞后结构的逼近：扩展AI 解读

Since a uniform approximation of distributed lag models by representatives of some subfamily of the family of all possible lag structures guarantees neither a reasonable standard error of forecast in large samples nor a good approximation of the true long-run response and mean lag, it is shown that the modified polynomial lags fulfill a stronger approximation property. A possible simplification of the estimation procedure for these models is mentioned.

经济事件的可预测性AI 解读

Events by Grunberg and Modigliani [3]. Economic forecasts are made to be used, and decisions based on them may affect their ultimate realization. Grunberg and Modigliani explored this problem in a model in which future aggregate supply was influenced by current decisions based on the predicted future price. They applied the Brouwer fixed point theorem to show that if the future equilibrium price is a bounded continuous function of its currently predicted value, a exists. In…