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多元自回归移动平均过程的拟合AI 解读

Akaike (1974) has shown that any autoregressive-moving average process admits a Markovian representation and conversely. There is a one-to-one correspondence between each autoregressive-moving average process and a member of a class of ‘special’ Markovian representations. Here we shall associate each of the above special representations with a uniquely defined ‘quasiautoregressive-moving average’ representation and we shall estimate the parameters involved by a technique…

一阶非循环自回归中的Edgeworth与鞍点近似AI 解读

The first-order noncircular autoregressive model is considered and Edgeworth and saddlepoint approximations are given for the distribution of the least squares estimator of the autoregressive coefficient. Numerical calculations are used to compare the two approximations with the exact distribution, found by numerical integration. Both approximations are unsatisfactory when the autoregressive coefficient is moderately large and the sample size small, the saddlepoint because…

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.

自回归模型阶数估计：max x 2 方法AI 解读

We develop a method of choosing the order of an autoregression to be used in conjunction with the subset autoregression technique (McClave 1975). A simulation is performed to compare this method (the max x 2 method) with Akaike's (1969, 1970) FPE technique of estimating order. The max x 2 outperforms FPE when used in conjunction with subset autoregression.

混合生成的离散时间序列（二）：渐近性质AI 解读

Summary The darma (discrete mixed autoregressive-moving average) processes are a broad but parametrically simple class of models for a stationary sequence of dependent discrete random variables. A darma process is formed as a random linear combination of independent identically distributed discrete random variables. The process is specified by the distribution of the independent variables, which is also the marginal distribution of the random process, and several other…

多重指数平滑中的矩阵求逆札记AI 解读

Summary In discussing the equivalence of certain polynomial predictors, Godolphin and Harrison (1975) note a matrix U employed in Multiple Exponential Smoothing whose inverse has not been obtained explicitly. The inverse of a related matrix p is obtained here and the relationship between the two matrices U and p reveals why no inverse has been obtained in general for U.

通过时域自回归模型拟合进行线性预测AI 解读

Let $\{x_t\}$ be a purely nondeterministic stationary process satisfying all the assumptions made by Berk (1974), and $\{y_t\}$ be another purely nondeterministic stationary process. Assume that $y_t$ is independent of $x_t$ but has exactly the same statistical properties as that of $x_t$. Consider the linear prediction of future values of $y_t$ on the basis of past values, using prediction constants estimated from a realisation of $T$ observations of $x_t$ by least-squares…

时间序列分析中的一致性AI 解读

A number of statistics that arise in time series analysis can be represented as the sum of a partial realization of a possibly serially dependent and nonstationary discrete-parameter stochastic process. The almost sure and $L_p, p > 1$, convergence of such statistics is investigated, under various moment conditions. The results are applied to the least squares estimates of multiple regressions.

不稳定过程边界参数估计量的渐近分布AI 解读

The limit distribution of the least squares estimator $\hat{\alpha}$ of the parameter $\alpha$ of the first order stochastic difference equation, in the boundary case $|\alpha| = 1$, is presented. With this, the asymptotic distributional problem for any real $\alpha$ in the first order case is completely settled.

计量经济模型的通用计算程序：SHAZAMAI 解读

to prepare and allow a large number of options. The program can be run in batch mode or interactively at a computer terminal. Computer core storage is dynamically allocated so that large problems are only limited by the size of the machine. SHAZAM is designed to grow so that new algorithms and procedures can easily be added by any programmer familiar with the internal structure of the program. Features of SHAZAM include ordinary least squares, two-stage least squares,…

工具变量估计方程中使用 Durbin h 检验的说明AI 解读

THE PURPOSE OF THIS PAPER is to consider the validity of Durbin's [1] h test when the h statistic is calculated from instrumental variable estimates of an autoregressive model. It seems useful to provide such an analysis since h tests based upon instrumental variable results have been reported in the empirical literature (for example, see McCallum [3]). The validity of the h test is investigated by deriving the asymptotic distribution (under the null hypothesis) of an…

自相关误差回归的极大似然估计程序AI 解读

The widely used Cochrane-Orcutt and Hildreth-Lu procedures for estimating the parameters of a linear regression model with first-order autocorrelation typically ignore the first observation. An alternative maximum likelihood procedure which incorporates the first observation and the stationarity condition of the error process is proposed in this paper. It is similar to the Cochrane-Orcutt procedure, and appears to be at least as computationally efficient. This estimator is…

谱估计量精确有限样本分布的近似AI 解读

In this paper an explicit and computationally convenient expansion of the exact finite sample distribution function of a quasi-maximum likelihood spectral estimator is given. In the majority of practical situations it will be necessary to estimate certain nuisance parameters of the distribution. Therefore, a method of evaluating these parameters is suggested and some Monte-Carlo evidence concerning the practical implementation of the results is given. 1 INTRODUCTfON AN…

关于时间序列分解的若干考察AI 解读

Suppose that an observable Gaussian time series Z1 can be written as the sum of an unobservable signal component Tt and a white noise component et. This paper proposes a procedure to estimate the Tt component uniquely by maximizing the variance of et with respect to a known model for Zt. Properties of this procedure are discussed and a comparison is made with a number of smoothing and filtering procedures commonly used in practice.

多元移动平均模型精确似然函数的计算AI 解读

This paper proposes three methods for computing the exact likelihood function of multivariate moving average models. Each method utilizes the structure of the covariance matrix in a different way. Formulae for operation counts of the three algorithms are given as a guide in selecting the best method for a given problem. Monte Carlo simulations are performed to compare the mean squared errors of parameter estimates obtained by maximizing the exact likelihood function versus…

线性模型自相关系数的修正最大似然估计量AI 解读

Two approximations to the maximum likelihood estimiator of the autocorrelation coefficient in first-order Markov disturbances in a linear model have been previously suggested by Durbin & Watson. A Monte Carlo study shows that one of these estimators is less absolutely biased and has smaller variance than the exact maximum likelihood estimator. Further, this estimator exhibits greater power in tests of autocorrelation when used in place of the standard Durbin-Watson…

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.

基于伪二次收敛准则的高斯移动平均修正极大似然估计AI 解读

A criterion is developed in this note for analysing the convergence properties of the direct representation for the maximum likelihood estimator of a Gaussian moving average. It is shown how this leads to a modified system for the estimator which is pseudoquadratically convergent. An illustration of the approach is given.

多元自回归移动平均过程的拟合AI 解读

Akaike (1974) has shown that any autoregressive-moving average process admits a Markovian representation and conversely. There is a one-to-one correspondence between each autoregressive-moving average process and a member of a class of ‘special’ Markovian representations. Here we shall associate each of the above special representations with a uniquely defined ‘quasiautoregressive-moving average’ representation and we shall estimate the parameters involved by a technique…

一阶非循环自回归中的 Edgeworth 与鞍点近似AI 解读

The first-order noncircular autoregressive model is considered and Edgeworth and saddlepoint approximations are given for the distribution of the least squares estimator of the autoregressive coefficient. Numerical calculations are used to compare the two approximations with the exact distribution, found by numerical integration. Both approximations are unsatisfactory when the autoregressive coefficient is moderately large and the sample size small, the saddlepoint because…

季节性时间序列模型偏自相关函数的解释AI 解读

A simple approach to understanding the behaviour of the partial autocorrelation function of seasonal time series is presented, based on a partial autocorrelation pattern. This pattern, which acts as a signature of the regular component of the model, is a simple composite of the autocorrelation and partial autocorrelation functions of the regular component.

预测误差方差的估计AI 解读

Spectral methods are used to construct an estimate of the variance of the prediction error for a normal, stationary process. The estimate obtained is shown to be strongly consistent and asymptotically normally distributed. Some aspects of the computations with respect to the fast Fourier transform are considered. The latter half of the article consists of a number of simulations, based on both generated and real data, which illustrate the results obtained. The relation…

自回归移动平均模型分析：估计与预测AI 解读

The exact likelihood function from a set of observations generated by univariate stationary normal autoregressive–moving average models is derived. Convenient methods are developed to evaluate the exact likelihood function, specifically the inverse and determinant of the T × T covariance matrix of the observations, ΣT and the quadratic form, Z′ΣT-1Z, where Z is a T × 1 vector of observations. Computations of the least squares and the maximum likelihood estimates of the…

针对自相关备择的随机性检验：替代方法AI 解读

The asymptotic efficiencies of the rank serial correlation and turning–points tests with respect to the serial correlation test are evaluated for first–order autocorrelation. Tests based on the periodogram of the data are suggested. A Monte Carlo study is conducted to evaluate the relative performance of likelihood derivative, distribution–free, and periodogram tests for small to moderate sample sizes with normal and nonnormal parent distributions. The serial correlation…