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自回归条件异方差与英国通胀方差估计AI 解读

Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced in this paper. These are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period…

平稳时间序列的一个刻画问题AI 解读

If a strictly stationary process $\{Z_k\}$ has residuals $Z_{k+1} - \sum^k_{j=1} a_{k,j}Z_j$ independent of $(Z_1, \cdots, Z_k)$ for all $k \geq m$, it is shown that the process is Gaussian or degenerate or $m$-step Markovian. Generalized (nonlinear) autoregressive stationary processes are defined and partially characterized.

有限阶自回归过程参数的 M 估计递归计算AI 解读

Stochastic approximation methods are used to generate a sequence of "$M$-estimates" for the unknown parameters of an autoregressive process of known, finite order which may have heavy-tailed innovations. Weak dependence properties, which can be demonstrated for many autoregressive processes, are used in the proof that the sequence converges almost surely to the parameters. A brief Monte Carlo study verifies that bounded influence functions provide protection for recursive…

具有相关残差的多项式趋势分类：贝叶斯方法AI 解读

Three procedures for the classification of multivariate time-dependent data are examined. Two are shown to be Bayes procedures assuming that the time dependence of the data can be described by polynomial regression functions and that the relation among successive residuals is described by a stationary and invertible ARMA process. Relative advantages of these procedures in practical applications and limitations of the model are discussed.

移动平均过程估计所用准则函数的比较AI 解读

It is well known that unconditional and conditional least squares estimators are asymptotically maximum likelihood for invertible moving average (MA) processes. By writing the criteria functions for these three estimators in comparable form, we establish simple inequalities between them and also between the corresponding disturbance variance estimates. Further analysis is carried out by examining the expected values of the criteria functions for given (true) coefficients in…

时间序列中三角函数成分的估计AI 解读

Estimation in time series with an unknown number of deterministic trigonometric components with unknown amplitudes and frequencies is considered. A stepwise procedure is used. At each step the frequency of the largest term in the periodogram of the residual series is used as a starting value for finding the best frequency in the least squares sense. The procedure is stopped when there are no further significant harmonic components, when tested by a multiple-test procedure.…

多个时间序列之间线性依赖与反馈的度量AI 解读

Measures of linear dependence and feedback for multiple time series are defined. The measure of linear dependence is the sum of the measure of linear feedback from the first series to the second, linear feedback from the second to the first, and instantaneous linear feedback. The measures are nonnegative, and zero only when feedback (causality) of the relevant type is absent. The measures of linear feedback from one series to another can be additively decomposed by…

具有相关残差的多元多项式趋势分类贝叶斯方法AI 解读

Three procedures for the classification of multivariate time-dependent data are examined. Two are shown to be Bayes procedures assuming that the time dependence of the data can be described by polynomial regression functions and that the relation among successive residuals is described by a stationary and invertible ARMA process. Relative advantages of these procedures in practical applications and limitations of the model are discussed.

移动平均过程估计中的准则函数AI 解读

It is well known that unconditional and conditional least squares estimators are asymptotically maximum likelihood for invertible moving average (MA) processes. By writing the criteria functions for these three estimators in comparable form, we establish simple inequalities between them and also between the corresponding disturbance variance estimates. Further analysis is carried out by examining the expected values of the criteria functions for given (true) coefficients in…

摘要暂缺

含缺失观测的平稳高斯 ARMA 过程的似然函数AI 解读

The likelihood function for an autoregressive-moving average process observed at n equally spaced time points has a well-known form. This note gives an expression for the likelihood function when some observations are missing from the series and shows how the missing observations may be estimated from the available data.

四阶累积量谱密度积分的估计AI 解读

It is known that the asymptotic variance of a quasimaximum likelihood estimate for a non-Gaussian process contains certain integrals of the fourth order cumulant spectral density. If we apply the asymptotic theory we are required to estimate these integrals. Here we shall propose some operational consistent estimates for them.

不连续决策过程与门限自回归时间序列建模AI 解读

Setting the problem of approximating an underlying nonlinear time series model within the framework of Bayesian decision theory, we demonstrate how the general analysis of discontinuous decision processes developed by Smith, Harrison & Zeeman (1981) leads naturally to a threshold autoregression.

递归残差的不变原理AI 解读

A general class of recursive residuals is defined by means of lower-triangular, orthonormal transformations. For these residuals, some weak invariance principles are established under appropriate regularity conditions. The theory is then incorporated in the study of robustness of some tests for change of parameters occurring at unknown time points.

自回归模型拟合中若干二次型的计算AI 解读

Let $\mathbf{R}$ be an infinite dimensional stationary covariance matrix, let $\mathbf{R}(k)$ and $\mathbf{W}(k)$ denote the top $k \times k$ left hand corners of $\mathbf{R}$ and $\mathbf{R}^{-1}$ respectively and let $\mathbf{\Sigma}(k)$ and $\mathbf{\Gamma}(k)$ denote the approximations for $\mathbf{R}(k)^{-1}$ suggested by Whittle (1951) and Shaman (1976) respectively. We consider quadratic forms of the type $Q(k) = \beta(k)' \mathbf{R}(k)^{-1}\alpha (k)$, when the…

多元时间序列模型的诊断检验AI 解读

This paper is concerned with the development and application of diagnostic checks for vector linear time series models. A hypothesis testing procedure based upon the score, or Lagrangean multiplier, principle is advocated and the distributions of the test statistic both under the null hypothesis and under a Pitman sequence of alternatives are discussed. Consideration of alternative models with singular sensitivity matrices when the null hypothesis is true leads to an…

随机回归模型的最小二乘估计及其在动态系统辨识与控制中的应用AI 解读

Strong consistency and asymptotic normality of least squares estimates in stochastic regression models are established under certain weak assumptions on the stochastic regressors and errors. We discuss applications of these results to interval estimation of the regression parameters and to recursive on-line identification and control schemes for linear dynamic systems.

季节调整的图形方法AI 解读

Graphical displays deserve to be a routine part of seasonal adjustment, and their routine use is now feasible because of the current revolution in computer graphical hardware and software. We present and illustrate seven graphical displays that provide powerful tools for judging the adequacy of the seasonal adjustment of a series and for understanding the behavior of the trend, seasonal, and irregular components.

时间序列变量间预测关系检验：蒙特卡洛研究AI 解读

Bivariate time series models have been used extensively to analyze the relationship between pairs of economic variables. Various tests have been proposed that can be used to examine the adequacy of specific models. The empirical literature is noteworthy for the frequency with which different authors using different tests reach different conclusions, and for the apparent lack of evidence for certain relationships strongly suggested by economic theory. The objective of this…

额外序列依赖下 Durbin–Watson 检验与 WLS 估计的表现AI 解读

Monte Carlo simulation is used to study the power of the Durbin-Watson test and the properties of the corresponding weighted least squares (WLS) estimates when there is serial correlation in the disturbance term, in addition to first-order autocorrelation. The results indicate that the Durbin-Watson test detects first-order autocorrelation, even when other forms of serial dependence are also present. However, routine use of WLS estimation when the Durbin-Watson test is…

基于 ARIMA 模型的季节调整方法AI 解读

This article proposes a model-based procedure to decompose a time series uniquely into mutually independent additive seasonal, trend, and irregular noise components. The series is assumed to follow the Gaussian ARIMA model. Properties of the procedure are discussed and an actual example is given.

额外序列依赖下 Durbin–Watson 检验与加权最小二乘的表现AI 解读

Monte Carlo simulation is used to study the power of the Durbin-Watson test and the properties of the corresponding weighted least squares (WLS) estimates when there is serial correlation in the disturbance term, in addition to first-order autocorrelation. The results indicate that the Durbin-Watson test detects first-order autocorrelation, even when other forms of serial dependence are also present. However, routine use of WLS estimation when the Durbin-Watson test is…

马尔可夫经济模型的不变分布与极限行为AI 解读

Equilibria in stochastic economic models are often time series which fluctuate in complex ways. But it is sometimes possible to summarize the long run, characteristics of these fluctuations. For example, if the law of motion determined by economic interactions is Markovian and if the equilibrium time series converges in a specific probabilistic sense then the long run behavior is completely determined by an invariant probability distribution. This paper develops and unifies…

含受限因变量模型估计量的渐近性质AI 解读

For the Tobit model with independent observations, Amemiya [1] has established the strong consistency and asymptotic normality of a stationary point, 9, of the log-likelihood. The likelihood for dependent observations may be computationally intractable, so the behavior of 9 in the presence of serially correlated observations is of interest. Under a relaxation of Amemiya's assumption of independence, we prove that 9 is strongly consistent and asymptotically normal, and give…