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不等间距空间数据的连续ARMA模型拟合AI 解读

Methods for fitting continuous spatial autoregressive moving average (ARMA) models to unequally spaced observations in two dimensions are reviewed and extended. These are models with rational two-dimensional spectra. Assuming Gaussian input noise and observational errors, maximum likelihood methods are used to estimate the ARMA parameters and the regression coefficients of the deterministic trend. When the number of observations is too large for exact maximum likelihood…

不等间距空间数据的连续 ARMA 模型拟合AI 解读

Methods for fitting continuous spatial autoregressive moving average (ARMA) models to unequally spaced observations in two dimensions are reviewed and extended. These are models with rational two-dimensional spectra. Assuming Gaussian input noise and observational errors, maximum likelihood methods are used to estimate the ARMA parameters and the regression coefficients of the deterministic trend. When the number of observations is too large for exact maximum likelihood…

不等间隔纵向数据中的序列相关AI 解读

Serial correlation in the within subject error structure in longitudinal data with unequally spaced observations is modelled using continuous time autoregressive moving averages. The models considered have both fixed and random effects in addition to serially correlated within subject errors. Two approaches are presented for calculating the exact likelihood for a model when the errors are Gaussian. The first calculates the covariance matrices for each subject for assumed…

不等间隔纵向数据中的序列相关AI 解读

Serial correlation in the within subject error structure in longitudinal data with unequally spaced observations is modelled using continuous time autoregressive moving averages. The models considered have both fixed and random effects in addition to serially correlated within subject errors. Two approaches are presented for calculating the exact likelihood for a model when the errors are Gaussian. The first calculates the covariance matrices for each subject for assumed…

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…

多元平稳时间序列创新广义方差的估计AI 解读

Recently there has been renewed interest in the nonparametric estimate of the innovation variance of a stationary time series. Empirical evidence has shown that some smoothing of the periodogram improves the estimate. This paper attempts to clarify the smoothing question and extends the results to the estimation of the innovation generalized variance of a multivariate stationary time series.

摘要暂缺

以随机场作为解释变量的回归AI 解读

The use of observations of a random function in space (random field) as independent variables in regression is considered including the numerical aspects. Details are presented for obtaining a numerical approximation to a Karhunen-Loève expansion when the random function is observed at a large number of points. The procedure involves a two stage modified principal component analysis. The dependent variable is then regressed on the principal components. An example from…

以随机场为解释变量的回归AI 解读

The use of observations of a random function in space (random field) as independent variables in regression is considered including the numerical aspects. Details are presented for obtaining a numerical approximation to a Karhunen-Loève expansion when the random function is observed at a large number of points. The procedure involves a two stage modified principal component analysis. The dependent variable is then regressed on the principal components. An example from…

摘要暂缺

平稳时间序列创新方差的估计AI 解读

The log of the periodogram is used to estimate the innovation variance of a stationary time series. The difference between the log of the estimated variance of the process and the log of the estimated innovation variance is used as a test for white noise. It is shown that this test is equivalent to Bartlett's test for homogeneity of variances applied to the periodogram without grouping and the asymptotic properties are derived.

摘要暂缺

具有周期结构的时间序列AI 解读

Time series which are encountered in meteorology exhibit non-stationary behaviour. If a variable is observed at the same time each day, it appears to be stationary over a period of a few weeks, but there is a seasonal variation in structure (Monin, 1963). For example, the mean and spectral density are different in the summer and in the winter. The usual approach to this problem is to divide the year into parts and analyse the data separately for the same two or three months…

具有平稳误差的多元回归AI 解读

A practical computing technique is presented for the joint estimation of regression coefficients and the error spectrum in regression problems with stationary errors. In problems where unweighted least squares is not efficient, the procedure gives an estimate approaching the minimum variance linear unbiased estimate. Whether unweighted least squares is nearly efficient or not efficient, the procedure, in general, gives a much closer estimate of the covariance matrix of the…

平稳误差下的多元回归AI 解读

A practical computing technique is presented for the joint estimation of regression coefficients and the error spectrum in regression problems with stationary errors. In problems where unweighted least squares is not efficient, the procedure gives an estimate approaching the minimum variance linear unbiased estimate. Whether unweighted least squares is nearly efficient or not efficient, the procedure, in general, gives a much closer estimate of the covariance matrix of the…

多元时间序列的指数平滑AI 解读

Summary A method is presented for estimating the optimum weight matrix for the exponential smoothing and prediction of multivariate time series. A recursive version of the estimation equations is given. A variation allows the estimation to forget the remote past in order to follow a process in which the structure varies slowly with time. It is pointed out that the method generalizes to non-linear processes when the non-linear structure is known. The practicality of the…