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多元时间序列的自相关与随机性检验AI 解读

There exist several tests for autocorrelation and randomness in multiple time series. Unfortunately, the exact distributions of these statistics are unknown and the asymptotic distributions that are known do not provide adequate approximation to the exact ones in small samples. In this article, the test statistics are modified. Asymptotically, these modified statistics are equivalent to their original counterparts; however, it is found that the asymptotic distributions of…

多元时间序列的自相关与随机性检验AI 解读

There exist several tests for autocorrelation and randomness in multiple time series. Unfortunately, the exact distributions of these statistics are unknown and the asymptotic distributions that are known do not provide adequate approximation to the exact ones in small samples. In this article, the test statistics are modified. Asymptotically, these modified statistics are equivalent to their original counterparts; however, it is found that the asymptotic distributions of…

自相关与随机性的 Durbin–Watson 及广义 Durbin–Watson 检验AI 解读

The Durbin–Watson (DW) test for lag 1 autocorrelation has been generalized (DWG) to test for autocorrelations at higher lags. This includes the Wallis test for lag 4 autocorrelation. These tests are also applicable to test for the important hypothesis of randomness. It is found that for small sample sizes a normal distribution or a scaled beta distribution by matching the first two moments approximates well the null distribution of the DW and DWG statistics. The…

异方差下两个线性回归系数集合相等的检验AI 解读

Structural shift is a common problem in a relationship dealing with time series data. Chow (1960) developed a test to detect such a shift under the assumption that observations both before and after the shift have the same variance. Structural shifts, however, often accompany changes in variance as well, and the Chow test is not robust to such changes. Two relatively robust tests are proposed and are found to be highly powerful.

异方差下两个线性回归系数集合的相等性检验AI 解读

Structural shift is a common problem in a relationship dealing with time series data. Chow (1960) developed a test to detect such a shift under the assumption that observations both before and after the shift have the same variance. Structural shifts, however, often accompany changes in variance as well, and the Chow test is not robust to such changes. Two relatively robust tests are proposed and are found to be highly powerful.

平稳自回归移动平均过程下样本自相关系数的分布AI 解读

This article examines the adequacy of approximations to the distributions of the sample autocorrelations by normal distributions, Edgeworth-type expansions, and four-parameter Pearson distributions. The accuracy of these approximations is found to depend critically on the data-generating process and sample size and to improve with sample size. Only the Pearson approximations seem to be reliable in relatively small samples. The utility of these approximations is illustrated…

Durbin–Watson统计量零假设分布与功效的近似AI 解读

It is computationally complex to obtain the exact distribution of the Durbin—Watson statistic for detecting autocorrelation in regression residuals. Moreover, the distribution cannot be tabulated once and for all because of its dependence on the regressors. It is found that the distribution can be well approximated by an appropriate. Pearson distribution which is computationally simple, easily programmed and seems to be valid when the regressors are commonly observed…

平稳时空过程的分析：估计与预测AI 解读

The paper analyses a simultaneous linear model representing stationary spatial-temporal processes. For processes with unit spatial orders, a simple method to compute the likelihood function is developed. Unfortunately, this technique does not generalize to higher order processes. Alternative methods applicable to higher order processes are developed. Finally, it is shown how predictions can be made over time if the parameters are known.

平稳时空过程分析：估计与预测AI 解读

The paper analyses a simultaneous linear model representing stationary spatial-temporal processes. For processes with unit spatial orders, a simple method to compute the likelihood function is developed. Unfortunately, this technique does not generalize to higher order processes. Alternative methods applicable to higher order processes are developed. Finally, it is shown how predictions can be made over time if the parameters are known.

自回归移动平均模型分析：估计与预测AI 解读

The exact likelihood function from a set of observations generated by univariate stationary normal autoregressive–moving average models is derived. Convenient methods are developed to evaluate the exact likelihood function, specifically the inverse and determinant of the T × T covariance matrix of the observations, ΣT and the quadratic form, Z′ΣT-1Z, where Z is a T × 1 vector of observations. Computations of the least squares and the maximum likelihood estimates of the…