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可逆短记忆与长记忆 ARIMA 模型差分参数的最大似然估计AI 解读

SUMMARY In practical applications of Box-Jenkins autoregressive integrated moving average (ARIMA) models, the number of times that the observed time series must be differenced to achieve approximate stationarity is usually determined by careful, but mostly informal, analysis of the differenced series. For many time series, some differencing seems appropriate, but taking the first or the second difference may be too strong. As an alternative, Hosking, and Granger and Joyeux…

通过广义线性回归拟合长记忆模型AI 解读

There is an increasing awareness of the importance of long-memory models in statistical applications.If long memory is present, it has to be taken into account in order to obtain reliable tests and confidence intervals.One obstacle to using models with long memory in routine statistical analysis has been the lack of easily available and sufficiently versatile statistical software.Here we propose a simple but flexible class of parametric models, which can be used to model…

通过广义线性回归拟合长记忆模型AI 解读

There is an increasing awareness of the importance of long-memory models in statistical applications. If long memory is present, it has to be taken into account in order to obtain reliable tests and confidence intervals. One obstacle to using models with long memory in routine statistical analysis has been the lack of easily available and sufficiently versatile statistical software. Here we propose a simple but flexible class of parametric models, which can be used to model…

长程相依时间序列的拟合优度检验AI 解读

SUMMARY We propose a test statistic for goodness of fit in time series with slowly decaying serial correlations. The asymptotic distribution of the test statistic, originally proposed by Milhoj for time series with smooth spectra, turns out to be the same, under the null hypothesis, even if the spectrum has a pole at 0. In particular, the test is suitable to detect lack of independence in the observations, or estimated residuals, if the first few correlations are small but…

缓慢衰减相关下的正态性检验与干扰参数AI 解读

Slowly decaying serial correlations can cause goodness-of-fit tests for a distribution to reject the null hypothesis with probability tending to one with increasing sample size. When the null distribution is completely specified (simple null hypothesis) the problem is actually worse than for the case where there are nuisance parameters to be estimated (composite null hypothesis). In particular, we consider here testing normality. We discuss limit theorems and propose…

缓慢衰减序列相关下高斯及相关过程的位置 M 估计AI 解读

We investigate the behavior of M estimators of the location parameter for stochastic processes with long-range dependence. The processes considered are Gaussian or one-dimensional transformations of Gaussian processes. It turns out that, up to a constant, all M estimators are asymptotically equivalent to the arithmetic mean. For Gaussian processes this constant is always equal to one, independently of the ψ function. In view of the case of iid observations, the results are…

序列相关缓慢衰减数据的位置参数检验AI 解读

Slowly decaying serial correlations have, if ignored, disastrous effects on classical tests and confidence intervals. We propose a modified t test for the location parameter which takes into account such correlations. An approximate distribution function of the test statistic is given under the assumption of fractional Gaussian noise. The results are generalized to prediction intervals for a future average. An example is given to illustrate the methods.