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傅里叶级数回归残差偏序列相关系数的近似分布AI 解读

Approximations are found to the joint distributions of noncircular and circular partial serial correlation coefficients calculated from residuals from regression on Fourier series. Results for coefficients calculated from deviations from the true mean and from the sample mean are obtained as special cases. It is shown that when the observations are independent the partial coefficients are approximately independently distributed in beta distributions that are the same for all…

充分估计量的密度近似AI 解读

A simple method of obtaining asymptotic expansions for the densities of sufficient estimators is described. It is an extension of the one developed by Barndorff-Nielsen & Cox (1979) for exponential families. A series expansion in powers of n−1 is derived of which the first term has an error of order n−1 which can effectively be reduced to n− / by renormalization.The results obtained are similar to those given by Daniels's (1954) saddlepoint method but the derivations are…

时间序列中的隐含周期性自回归移动平均模型AI 解读

Some properties of a class of periodic models for characterizing seasonal time series are explored. The relationships between periodic models and multiple autoregressive-moving average models are developed and used to gain insight into the behaviour of periodic models. In particular it is shown how homogeneous autoregressive-moving average models may be mistakenly specified for series in which periodic properties are present. Consequences of such misspecification on…

零一观测变点问题的简单累积和型统计量AI 解读

A simple cumulative sum type statistic for the change-point with zero-one observations is introduced. A conditional test of no change against change is introduced and compared with a likelihood ratio test. The estimation of the change-point is also considered, using the simple statistic, and the method is shown to be asymptotically equivalent to the maximum likelihood estimator in certain circumstances and almost equivalent in others. To investigate the small sample…

利用未知水平的上穿越估计频率AI 解读

By counting the number of upcrossings of the mean level by a stationary Gaussian process one can estimate the mean frequency of the process. Here we present a frequency estimator based on the number of upcrossings of one unknown level hoped to be near the mean, and the percentage of the total observation time spent above the level. This is equivalent to observing upcrossings of a known level in a process with unknown mean and variance. Formulae are given for the bias and…

角度观测依赖的二元模型及相关马尔可夫过程AI 解读

Some new distributions having specified marginal distributions are proposed for dependent random variables taking values on the torus. A related family of Markov processes taking values on the circle is constructed, and statistical inference for these processes is studied.

高阶 ARMA 过程精确似然的计算算法AI 解读

The likelihood function for an autoregressive-moving average process is obtained using Kalman filtering and an algorithm of Morf, Sidhu & Kailath (1974). It is shown that this method is more efficient than others in the literature when the order of the moving average part is greater than five.

多元移动平均过程自协方差的有效估计AI 解读

This paper proposes a method for estimating the autocovariances of a d-dimensional moving average process of order q. The estimators have the same asymptotic covariance matrix as those obtained by maximizing a Gaussian likelihood, and are obtained by performing a generalized least squares regression of the periodogram on the autocovariance, thus extending Parzen's (1971) estimators for d = 1. (Author)

ARMA 过程样本逆自相关的渐近分布AI 解读

The inverse autocorrelations of a time series are useful at the identification stage of model building. In practice these quantities must be estimated from the data and so the distributional properties of the estimators are of great importance. In this paper the asymptotic distribution of the sample inverse autocorrelations is derived, making use of the duality between the autocorrelations and inverse autocorrelations of two autoregressive-moving average processes.

干预分析与多元时间序列AI 解读

A general model is introduced to encapsulate interventions in a multiple time series. The estimation of this model is discussed, and a bivariate economic example is presented to illustrate the methods.

单变量 ARMA 时间序列模型残差互相关的分布AI 解读

Cross-correlations between univariate autoregressive moving average (ARMA) time series residuals are useful in the examination of relationships between time series (Pierce 1977a) and in the identification of dynamic regression models (Haugh and Box 1977). In this article, the asymptotic distribution of these residual cross-correlations is derived, and its application to the problem of testing for lagged relationships in the presence of instantaneous causality is discussed.…

时间序列的决定系数度量AI 解读

With time series data, the conventional regression R 2 is a nebulous concept, as the explained variation consists in part of variation that can be attributed merely to past values of the dependent variable. Thus R 2 is extremely sensitive to prefiltering operations such as first differencing. This article develops and illustrates an alternative R 2 concept, which eliminates this ambiguity by measuring the explanatory power of a time series-regression model relative to that…

关于自回归移动平均模型识别的一则札记AI 解读

A discussion is given of the identification and parameterization of autoregressive-moving average systems in relation to the use of certain canonical forms.

利用样本自协方差估计自回归移动平均模型参数AI 解读

This paper generalizes the work of Godolphin (1977, 1978) for estimating parameters of the moving average model and of the general autoregressive moving average model by solving the approximate log likelihood equation of Walker (1964).

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.

向量自回归模型的渐近预测均方误差AI 解读

This paper derives the asymptotic mean squared error of multistep prediction for the general vector autoregressive process. For one-step-ahead prediction the result is a surprisingly simple generalization of the result for the scalar autoregressive process. Results for multistep prediction are also derived for the regression model with autoregressive errors, where the set of exogenous variables follows a vector autoregressive process.

自回归移动平均模型中残差自相关的有限样本分布AI 解读

We examine by simulation the finite sample properties of tests of model adequacy based on individual residual autocorrelations, and of portmanteau statistics based on several residual autocorrelations, for autoregressive-moving average models. Both nonseasonal and seasonal models are considered.

非平稳时间序列中的信号提取误差AI 解读

It is supposed that an observable time series $\{x_t\}$ is representable as the sum of a "signal" $s_t$ and a "noise" $n_t$, and that it is desired to extract the signal $s_t$, i.e., to obtain an estimate $\hat{s}_t$ of $s_t$. Corresponding to any such estimate is a signal extraction error, $\delta_t = s_t - \hat{s}_t$, which for nondeterministic stochastic processes possesses a nonzero mean square. For the class of homogeneously nonstationary processes, characterizations of…

具有相关误差的一般线性模型的递归估计AI 解读

Summary The techniques for recursive estimation of the general linear model are extended to the case of dependent errors with known second-order properties. Recurrence relations for computation and a sequence of independent recursive residuals, useful for testing the constancy of the regression relation over time, are derived and studied. Computational savings are available when the error process is stationary.

含单位根的自回归过程估计AI 解读

Let $Y_t$ satisfy the stochastic difference equation $Y_t = \sum^p_{j = 1}\eta_jY_{t - j} + e_t$ for $t = 1, 2, \cdots$, where the $e_t$ are independent identically distributed $(0, \sigma^2)$ random variables and the initial conditions $(Y_{-p + 1}, Y_{-p + 2}, \cdots, Y_0)$ are fixed constants. It is assumed the true, but unknown, roots $m_1, m_2, \cdots, m_p$ of $m^p - \sum^p_{j = 1}\eta_jm^{p - j} = 0$ satisfy $m_1 = m_2 = 1$ and $|m_j| < 1$ for $j = 3, 4, \cdots, p$.…

平稳多元自回归移动平均模型的似然函数AI 解读

Procedures to estimate parameters in multivariate autoregressive moving average (ARMA) models are developed. Gaussian errors are assumed. Exact maximum likelihood estimation procedures are developed for pure moving average models. Approximate procedures are obtained to estimate stationary mixed ARMA models. Properties of the estimates and an example are given.

有限总体中的复合估计AI 解读

It is common practice in large recurring surveys to employ rotation sampling schemes. Composite estimators are often used in association with rotation schemes to reduce the variability of the survey estimators. In this article, expressions for the variances of certain composite estimators are derived. It is demonstrated how the variance expressions may be used in planning panel surveys and in certain time series analyses. This work is illustrated by the Census Bureau's…

计量经济模型的统计分析AI 解读

In this article, a summary of some research bearing on the statistical analysis of econometric models is reviewed. Many estimation, testing, and prediction techniques used in econometrics have just large-sample justifications. Selected Bayesian inference results relating to econometric models are reviewed. On the problem of constructing econometric models, an approach that is a blend of traditional econometric and modern time series analysis techniques is described. Many…

加拿大货币与收入数据的自回归建模AI 解读

A sequential procedure based on Akaike's final prediction-error criterion and Granger's concept of causality to fit multiple auto-regressions is suggested. The method not only allows each variable to enter the equation with a different time lag but also provides a reasonably powerful test of exogeneity or causality. The idea is applied to Canadian postwar money and income data. It is found that a bivariate feedback model for M1 and GNP and a one-way causal relation from GNP…