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滞后回归残差与序列相关检验AI 解读

A new family of statistics is proposed to test for the presence of serial correlation in linear regression models. The tests are based on partial sums of lagged cross-products of regression residuals that define a class of interesting Gaussian processes. These processes are characterized in terms of regressor functions, the serial-correlation structure, the distribution of the noise process, and the order of the lag of the cross-products of residuals. It is shown that these…

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多项式回归残差部分和的性质及未知时点回归变化检验AI 解读

Limit processes are obtained for the sequences of partial sums of polynomial regression residuals. Properties of linear and quadratic functionals on the sequences are discussed. Distribution theory for Cramer-von Mises type functionals is obtained. An indication is given of the relevance of these results to the problem of testing for change of regression at unknown times.

检验多个时间序列是否共享周期AI 解读

Tests are discussed for detecting the presence of common periodicities in the components of a multiple time series. Distributional results are obtained for the case of white noise, independent, normal series. These are extended, first to the case of normal linear series with specified spectra and then to the case of estimated spectra. These results are then discussed in the context of correlated series. The tests are applied to several sets of data.

检验多条时间序列是否具有共同周期AI 解读

Tests are discussed for detecting the presence of common periodicities in the components of a multiple time series. Distributional results are obtained for the case of white noise, independent, normal series. These are extended, first to the case of normal linear series with specified spectra and then to the case of estimated spectra. These results are then discussed in the context of correlated series. The tests are applied to several sets of data.

未知时点的参数变化检验及相关布朗运动泛函的分布AI 解读

Statistics are derived for testing a sequence of observations from an exponential-type distribution for no change in parameter against possible two-sided alternatives involving parameter changes at unknown points. The test statistic can be chosen to have high power against certain of a variety of alternatives. Conditions on functionals on $C\lbrack 0,1\rbrack$ are given under which one can assert that the large sample distribution of the test statistic under the…

多元时间序列周期成分的检验AI 解读

The problem of testing for periodicities in multiple time series is considered. The test statistic proposed is based on the Euclidean norm of the matrix of periodograms. We first obtain the exact distribution of our test statistic under the hypothesis that observations are taken from an n-vector time series consisting of independent series of independent normal variables. We extend the theory to normal linear series with a specified spectral density matrix and then show that…

多元时间序列周期成分的检验AI 解读

The problem of testing for periodicities in multiple time series is considered. The test statistic proposed is based on the Euclidean norm of the matrix of periodograms. We first obtain the exact distribution of our test statistic under the hypothesis that observations are taken from an n-vector time series consisting of independent series of independent normal variables. We extend the theory to normal linear series with a specified spectral density matrix and then show that…