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单调增益、一阶自相关与过零率AI 解读

The effect of a linear filter with monotone gain on the first-order autocorrelation of a weakly stationary time series is discussed. When the gain is monotone increasing, the first-order autocorrelation cannot increase. Otherwise, when the gain is monotone decreasing, the correlation cannot decrease. Further, when the gain is strictly monotone, the first-order autocorrelation is unchanged if and only if the process is a pure sinusoid with probability 1. Under the Gaussian…

高阶穿越的渐近方差及其在快速白噪声检验中的应用AI 解读

The rate of decrease in the variance of higher order crossings is obtained for stationary m-dependent Gaussian sequences. This result provides a quick approximation to the variance of the number of axis-crossings of m-dependent processes, and is applied in determining approximate probability limits for the higher order crossings of white noise. The limits are used in testing for white noise in simulated and also real data examples.

高阶交叉的渐近方差及其快速白噪声检验应用AI 解读

The rate of decrease in the variance of higher order crossings is obtained for stationary m-dependent Gaussian sequences. This result provides a quick approximation to the variance of the number of axis-crossings of m-dependent processes, and is applied in determining approximate probability limits for the higher order crossings of white noise. The limits are used in testing for white noise in simulated and also real data examples.

平稳时间序列的正弦极限AI 解读

We show that the Sinusoidal Limit Theorem of Slutsky in the Gaussian case is a consequence of the equality of certain higher order crossings.

利用高阶过轴次数辨别时间序列AI 解读

A new methodology is proposed for discrimination among stationary time-series. The time series are transformed into binary arrays by clipping (retaining only the signs of) the $j$th difference series, $j = 0, 1, 2, \cdots$. The degeneracy of clipped $j$th differences is studied as $j$ becomes large. A new goodness of fit statistic is defined as a quadratic form in the counts of axis-crossings by each of the first $k$ differences of the series. Simulations and the degeneracy…

时间序列模型的拟合优度：高阶穿越的应用AI 解读

A relation between the graphical appearance of a stationary time series and its autocorrelations is discussed. The use of counts of visual features termed higher order crossings is proposed in testing goodness of fit of hypothesized models against very general alternatives. Attention is focused on a specific example of a new type of nonparametric test statistic arising from iterative feature extraction procedures called extractors. The statistic is compared with Box &…

时间序列模型拟合优度：高阶交叉的应用AI 解读

A relation between the graphical appearance of a stationary time series and its autocorrelations is discussed. The use of counts of visual features termed higher order crossings is proposed in testing goodness of fit of hypothesized models against very general alternatives. Attention is focused on a specific example of a new type of nonparametric test statistic arising from iterative feature extraction procedures called extractors. The statistic is compared with Box &…

硬限幅后平稳自回归过程的参数估计AI 解读

Estimates of the parameters in normal autoregressive (AR(p)) processes may be obtained as functions of certain runs and subsequences in the associated clipped 0 − 1 processes. For example, the parameter in AR (1) is a function of the number of 1 runs only. Equivalently, this parameter can be estimated by counting only the number of axis crossings by the process. The estimates are obtained by a modification of the likelihood function of the clipped data. The loss of…

充分性与平稳过程的水平穿越次数AI 解读

It is shown how to derive the exact distribution of the number of axis crossings by a stationary process when the binary process obtained by clipping the original process is a pth-order Markov chain. The same method is used in deriving the asymptotic distribution of the number of upcrossings of a high level by a stationary process.

平稳过程的充分性与水平穿越次数AI 解读

It is shown how to derive the exact distribution of the number of axis crossings by a stationary process when the binary process obtained by clipping the original process is a pth-order Markov chain. The same method is used in deriving the asymptotic distribution of the number of upcrossings of a high level by a stationary process.

两状态二阶马尔可夫链的充分统计量AI 解读

Statistical inference for binomial processes with second-order Markov dependence is worked out. Sufficient statistics for the 2 2 parameters associated with the process are found and their exact joint distribution is given in a closed form. An algorithm for finding the probability of k successes in n dependent trials is developed and a simple estimation procedure is suggested and applied to a meteorological time series.

两状态二阶马尔可夫链的充分统计量AI 解读

Statistical inference for binomial processes with second-order Markov dependence is worked out. Sufficient statistics for the 2 2 parameters associated with the process are found and their exact joint distribution is given in a closed form. An algorithm for finding the probability of k successes in n dependent trials is developed and a simple estimation procedure is suggested and applied to a meteorological time series.