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利用样本自相关估计时间序列参数AI 解读

SUMMARY Consider a scalar linear process {xt} whose spectral density is σ 2 k(λ, θ 0) where σ2 is the innovation variance and k(⋅,θ0)∈{k(⋅,θ):θ∈S⊂ℝq}. We introduce a class of estimators of θ0 based only on the sample autocorrelations. These estimators are shown to be consistent and asymptotically normally distributed with a covariance matrix which is independent of the distributions of the innovations. A lower bound to the asymptotic covariances of these estimators is…

列联表中的序列依赖AI 解读

SUMMARY A simple and useful representation is given for the asymptotic behaviour of the Pearson χ 2 test of independence in two-way contingency tables. This is used to analyse the statistic when the data are generated by Markov chains. A robustness result, showing when the Markov dependence has no effect on the usual limiting χ2 distribution, is also given.

AR(p)模型对含测量误差AR(p)模型的单侧拉格朗日乘子检验AI 解读

SUMMARY The one-sided Lagrange multiplier test is suggested for testing the null autoregressive (AR) model against the AR model with measurement error. The test statistic is shown to be asymptotically N(0, 1) under the null. Finite sample properties of the test both under the null and under the alternative are examined briefly by simulations.

ARMA 模型中自回归参数最小二乘估计的一致性AI 解读

A unified treatment of the consistency properties of the ordinary least squares estimates in an autoregressive fitting of time series from nonstationary or stationary autoregressive moving average models is given. For a given model, the orders of autoregressions which produce consistent estimates are obtained and the limiting values, hence the biases, of the estimates of other autoregressions are investigated.

时间序列过去与未来的典型相关：界与计算AI 解读

This paper continues an investigation into the canonical correlations and canonical components of the past and future of a stationary Gaussian time series which were introduced in Jewell and Bloomfield (1983). Bounds for the maximum canonical correlation are provided under specified conditions on the spectrum of the series. A computational scheme is described for estimating the canonical correlations and components and the procedure is illustrated on the well-known sunspot…

时间序列过去与未来的典型相关：定义与理论AI 解读

The concepts of canonical correlations and canonical components are familiar ideas in multivariate statistics. In this paper we extend these notions to stationary time series with a view to determining the most predictable aspect of the future of a time series. We relate properties of the canonical description of a time series to well known structural properties of the series such as (i) rational spectra (i.e., ARMA series), (ii) strong mixing, (iii) absolute regularity, etc.

利用拉格朗日乘数检验估计ARMA模型阶数AI 解读

A stepwise testing procedure using Lagrangian multiplier tests is developed to determine the order of an ARMA-process. The strong consistency of this procedure under slightly weaker assumptions than in Hannan (1980) (proof of the consistency of the order estimators obtained via BIC) is proved.

广义条件下回归函数核估计的一致收敛AI 解读

In this article we prove uniform consistency of kernel estimators of a multivariate regression function under various assumptions on the distribution of the data. In addition to the usual assumptions that the data are iid and that the distribution of the regressors is absolutely continuous, we consider the cases that some regressors are discrete and the data are either stationary ϕ-mixing themselves or generated by a class of functions of one-sided infinite stationary…

含日历变动的时间序列建模AI 解读

The modeling of time series data that include calendar variation is considered. Autocorrelation, trends, and seasonality are modeled by ARIMA models. Trading day variation and Easter holiday variation are modeled by regression-type models. The overall model is a sum of ARIMA and regression models. Methods of identification, estimation, inference, and diagnostic checking are discussed. The ideas are illustrated through actual examples.

Durbin 显著性检验的推广及其在动态设定中的应用AI 解读

When estimating a single equation with an error generated by an autoregressive process of higher order than one using a sequence of likelihood ratio tests to determine the correct order, the asymptotic size of the tests will be biased because of multiple optima of the likelihood function. A new type is suggested similar to the Durbin test [2] which is not biased in this way. IN HIS ARTICLE on testing for serial correlation in the presence of lagged endogenous variables [2]…

扩展有理逼近（ERA）：小样本理论的新方法AI 解读

This article proposes a new approach to small sample theory that achieves a meaningful integration of earlier directions of research in this field. The approach centers on the constructive technique of approximating distributions developed recently by the author in [10]. This technique utilizes extended rational approximants (ERA's) which methods (such as those based on asymptotic expansions) and which simultaneously blend information from diverse analytic, numerical and…

二项概率变化的似然比与累积和检验功效AI 解读

A simple iterative procedure is found for the exact null and alternative distributions of likelihood ratio, cumulative sum and related statistics for testing for a change in probability of a sequence of independent binomial random variables. It is concluded that the likelihood ratio test is slightly less powerful than the cumulative sum test near the middle of the sequence, but that the likelihood ratio test is much more powerful near the ends. An example from epidemiology…

平稳随机过程的 m 阶最大似然估计AI 解读

SUMMARY Sometimes the likelihood cannot be computed even introducing approximations whose effect is asymptotically negligible. To overcome this problem for inference from a stochastic process, we approximate the log likelihood by a sum whose generic term is the density function of the corresponding sample element conditional on the m most recent observations, for some m ≥ 0. General results on the asymptotic properties of the associated estimates are given, and numerical…

ARMAX 系统参数化的性质及其对结构估计与动态设定的意义AI 解读

ARMAX systems in structural specification are considered. Topological and geometric properties of the parameter space and of the parameterization which are important for the properties of the estimators, regardless of their special form, are investigated and the specification of the maximum lag lengths is discussed.

利用相关序列进行数据分解AI 解读

Quarterly real GNP and implicit GNP deflator series are derived for the 1948–1970 period using the related series technique of Chow and Lin. These estimated series are compared with the official, revised series; to official, unrevised series; and to univariate proxies using regression, time series, and spectral methods. The derived series possess autocorrelation and turning point characteristics similar to those of the official, revised series. The derived series also…

含趋势与季节性的时间序列预测AI 解读

A maximization of the expected entropy of the predictive distribution interpretation of Akaike's minimum AIC procedure is exploited for the modeling and prediction of time series with trend and seasonal mean value functions and stationary covariances. The AIC criterion best one-step-ahead and best twelve-step-ahead prediction models can be different. The different models exhibit the relative optimality properties for which they were designed. The results are related to open…

自回归参数的固定精度估计AI 解读

For a first order non-explosive autoregressive process with unknown parameter $\beta \in \lbrack -1, 1 \rbrack$, it is shown that if data are collected according to a particular stopping rule, the least squares estimator of $\beta$ is asymptotically normally distributed uniformly in $\beta$. In the case of normal residuals, the stopping rule may be interpreted as sampling until the observed Fisher information reaches a preassigned level. The situation is contrasted with the…

自回归误差回归模型预测的小样本性质AI 解读

Monte Carlo methods are used to examine the small-sample properties of various estimators of asymptotic prediction variance (APV) from the regression model with autoregressive errors. Two practical estimators of APV, one of which includes terms reflecting parameter estimation and one of which excludes these terms, are compared to the mean squared error of prediction for regression models with different autocorrelation of the errors, different sample sizes, and different…

自回归误差回归模型预测的小样本性质AI 解读

Monte Carlo methods are used to examine the small-sample properties of various estimators of asymptotic prediction variance (APV) from the regression model with autoregressive errors. Two practical estimators of APV, one of which includes terms reflecting parameter estimation and one of which excludes these terms, are compared to the mean squared error of prediction for regression models with different autocorrelation of the errors, different sample sizes, and different…

一阶移动平均误差的根位于单位圆时的回归模型极大似然估计AI 解读

J. D. Sargan, Alok Bhargava, Maximum Likelihood Estimation of Regression Models with First Order Moving Average Errors when the Root Lies on the Unit Circle, Econometrica, Vol. 51, No. 3 (May, 1983), pp. 799-820

使用预定但非严格外生工具变量的时间序列模型近有效估计AI 解读

Particularly under the assumption of rational expectations, a model may have serially correlated errors and those errors may be uncorrelated with contemporaneous and lagged values of a predetermined instrument, yet the instruments may not be strictly exogenous. This paper proposes a method for transforming such a model to one without serial correlation, while keeping the instrument predetermined. Standard theory of instrumental variables estimation then applies. Furthermore,…

存在缺失或聚合数据时向量ARMA过程的精确似然AI 解读

This note points out that by using the Kalman filter with nonconstant coefficients, we can compute the exact likelihood of an autoregressive-moving average process observed with noise, when some of our observations are either missing or aggregated.

时间序列模型的后验赔率AI 解读

This paper is concerned with model selection in time series analysis. A Bayesian approach is adopted to investigate various decision criteria previously advocated. The discussion is conducted in the context of a class of nonlinear time series models of sufficient generality to encompass a wide range of processes currently of interest.

多元自回归指数模型的若干结果AI 解读

We discuss methods for modelling multivariate autoregressive time series in terms of a smaller number of index series which are chosen to provide as complete a summary as possible of the past information contained in the original series necessary for prediction purposes. The maximum likelihood method of estimation and asymptotic properties of estimators of the coefficients which determine the index variables, a well as the corresponding autoregressive coefficients, are…