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移动平均算子特征多项式具有单位零点时的ARMA参数估计AI 解读

We consider the estimation of parameters in the time series model $X(t) = \sum^q_{j = 1}a_jX(t - j) + \varepsilon(t) - \varepsilon(t - j) - \sum^p_{j = 1} c_j\{\varepsilon(t - j) - \varepsilon(t - j - 1)\}$ where the $\varepsilon(t)$ are independently identically distributed random variables with zero mean and variance $\sigma^2$. We compute the exact $\log$ likelihood of the model, propose and justify an asymptotic approximation of it. The latter will be used to derive…

周期自回归与多元自回归的分析AI 解读

A methodology is presented for analyzing periodic autoregressions which is also applicable when inferring the second order properties of periodically correlated processes. In addition, capitalizing on the connection between periodic and multiple autoregressions, a method is set forth for analyzing the latter, which overcomes the usual requirements of a large number of both parameters and computer storage locations. This is achieved by introducing an orthogonal…

回归变量含滞后因变量时对一般自回归与移动平均误差模型的检验AI 解读

Since dynamic regression equations are often obtained from rational distributed lag models and include several lagged values of the dependent variable as regressors, high order serial correlation in the disturbances is frequently a more plausible alternative to the assumption of serial independence than the usual first order autoregressive error model. The purpose of this paper is to examine the problem of testing against general autoregressive and moving average error…

混合生成的离散时间序列（一）：相关与游程性质AI 解读

Summary A broad but parametrically simple model for a stationary sequence of dependent discrete random variables is given and several submodels are discussed. The structure of the model is specified by the marginal distribution of the random variables and several other parameters. The sequence of random variables is formed by a probabilistic linear combination of i.i.d. discrete random variables and is in general not Markovian. Second-order joint moments and spectra are…

含常数项回归中正系数一阶自回归情形下 σ² 最小二乘估计量的偏差界AI 解读

H. Neudecker, Bounds for the Bias of the LS Estimator of σ 2 in the Case of a First-Order (Positive) Autoregressive Process when the Regression Contains a Constant Term, Econometrica, Vol. 46, No. 5 (Sep., 1978), pp. 1223-1226

平稳时间序列的预测方差及相关统计量AI 解读

A spectral estimate of the generalized prediction variance of a stationary time series is considered and a modification which uses a frequency domain regression to allow for the effect of exogenous variables is introduced. Strong consistency and a central limit theorem are proved for this estimate and for several statistics derived from it. The results of some simulations are presented, together with the results of application to two published sets of data

尼罗河问题：变点问题的条件解AI 解读

Inference is considered for the point in a sequence of random variables at which the probability distribution changes. An approximation to the conditional distribution of the maximum likelihood estimator of the changepoint given the ancillary values of observations adjacent to the estimated changepoint is derived and shown to be numerically equal to a Bayesian posterior distribution for the changepoint. A hydrological example is given to show that inferences based on the…

时间序列模型拟合不足的一种度量AI 解读

The overall test for lack of fit in autoregressive-moving average models proposed by Box & Pierce (1970) is considered. It is shown that a substantially improved approximation results from a simple modification of this test. Some consideration is given to the power of such tests and their robustness when the innovations are nonnormal. Similar modifications in the overall tests used for transfer function-noise models are proposed

平稳时间序列的预测方差及相关统计量AI 解读

A spectral estimate of the generalized prediction variance of a stationary time series is considered and a modification which uses a frequency domain regression to allow for the effect of exogenous variables is introduced. Strong consistency and a central limit theorem are proved for this estimate and for several statistics derived from it. The results of some simulations are presented, together with the results of application to two published sets of data

自回归时间序列拟合优度统计量渐近分布的统一推导AI 解读

Summary The portmanteau and Quenouille goodness-of-fit tests for an ar(p) model are derived as likelihood-ratio tests against particular alternative hypotheses, and their asymptotic distributions are thereby obtained.

Box–Jenkins模型残差自相关的分布AI 解读

Summary The large sample distribution of the residual autocorrelations in the arma model is derived. The main advantage of this derivation over that of Box and Pierce (1970) is that it extends directly to more general situations. Generalizations of the derived distribution are presented for the residual autocorrelations in the multiplicative seasonal arma model and for the autocorrelations of a subseries of the residuals.

检测移动平均模型系数空缺的大样本检验AI 解读

Summary A procedure is given in the paper for testing the hypothesis that a specified set of parameters in a moving average process assumes the value zero. In particular, the method is applicable for detecting whether a moving average process is seasonal or not. This large-sample test, which operates entirely in the time domain, is based on the estimated asymptotic covariance matrix of improved estimates of the autocorrelation function and is derived from the results of…

自回归依赖下的单样本秩检验AI 解读

One-sample linear rank tests are considered for the case where the observations are not independent but come from an autoregressive process. It is proposed to apply the tests under these circumstances to certain transformations of the observations, rather than to the observations themselves. Then the tests have asymptotically the same properties as under independence, both under the hypothesis and under contiguous location alternatives. In particular, they are asymptotically…

回归中的季节性：平滑先验的应用AI 解读

This article argues that conventional approaches to the treatment of seasonality in econometric investigation are often inappropriate. A more appropriate technique is to allow all regression coefficients to vary with the season, but to constrain them to do so in a smooth fashion. A Bayesian method of estimating smoothly varying seasonal coefficients is developed, based on Shiller's (1973) approach to estimating distributed lags. In a sampling experiment, this technique…

自回归过程的重复测量AI 解读

Estimation of parameters and tests of hypotheses are studied in first-order autoregressive processes where the process is observed several times over a given time interval. The process may be homogeneous (i.e., the parameters may be constant over time) or inhomogeneous (time-varying parameters). Sufficient statistics under normality are obtained for various cases and several tests of hypotheses are given.

信息有限条件下的预测：平车载拖车运输市场的 ARIMA 模型AI 解读

This paper evaluates the appropriateness of autoregressive integrated moving average (ARIMA) time-series models for forecasting in information-scarce environments. Such environments are defined and a specific transportation sector example examined. It is shown that ARIMA models adequately characterize economic activity in this example. ARIMA model forecasts are seen to dominate alternative models, and to provide information required for market efficiency. Specific attention…

有限信息下的预测：铁路平车载拖车运输市场的 ARIMA 模型AI 解读

This paper evaluates the appropriateness of autoregressive integrated moving average (ARIMA) time-series models for forecasting in information-scarce environments. Such environments are defined and a specific transportation sector example examined. It is shown that ARIMA models adequately characterize economic activity in this example. ARIMA model forecasts are seen to dominate alternative models, and to provide information required for market efficiency. Specific attention…

回归中的季节性：平滑先验的应用AI 解读

This article argues that conventional approaches to the treatment of seasonality in econometric investigation are often inappropriate. A more appropriate technique is to allow all regression coefficients to vary with the season, but to constrain them to do so in a smooth fashion. A Bayesian method of estimating smoothly varying seasonal coefficients is developed, based on Shiller's (1973) approach to estimating distributed lags. In a sampling experiment, this technique…

用偏自相关矩阵刻画协方差函数AI 解读

It is known that the autocorrelation function of a stationary discrete-time scalar process can be uniquely characterized by the so-called partial autocorrelation function, which is a sequence of numbers less or equal to one in magnitude. We show here that the matrix covariance function of a multivariate stationary process can be characterized by a sequence of matrix partial correlations, having singular values less than or equal to one in magnitude. This characterization can…

随机过程的条件最小二乘估计AI 解读

An estimation procedure for stochastic processes based on the minimization of a sum of squared deviations about conditional expectations is developed. Strong consistency, asymptotic joint normality and an iterated logarithm rate of convergence are shown to hold for the estimators under a variety of conditions. Special attention is given to the widely studied cases of stationary ergodic processes and Markov processes with are asymptotically stationary and ergodic. The…

充分性与平稳过程的水平穿越次数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.

利用伪二次收敛准则修正高斯移动平均模型的最大似然估计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.

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.