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A Tukey nonadditivity-type test for time series nonlinearity

时间序列非线性的 Tukey 非可加性型检验

The most general form of a nonlinear strictly stationary process is that referred to as a Volterra expansion; this is to a linear process what a polynomial is to a linear function. Because of this similarity, an analogue of Tukey's one degree of freedom for non-additivity test is constructed as a test for linearity versus a second-order Volterra expansion.

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Estimation of a Noisy Discrete-Time Step Function: Bayes and Empirical Bayes Approaches

含噪离散时间阶梯函数的贝叶斯与经验贝叶斯估计

Consider the problem of estimating, in a Bayesian framework and in the presence of additive Gaussian noise, a signal which is a step function. Best linear estimates and Bayes estimates are derived, evaluated and compared. A characterization of the Bayes estimates is presented. This characterization has an intuitive interpretation and also provides a way to compute the Bayes estimates with a number of operations of the order of $T^3$ where $T$ is the fixed time span. An…

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Order Selection in Nonstationary Autoregressive Models

非平稳自回归模型的阶数选择

In Hannan (1980), some limiting properties of the order selection criteria, AIC, BIC, and $\phi(p, q)$ for modeling stationary time series were derived. In this paper, we generalize these properties to the case in which the underlying process follows a nonstationary autoregressive model. We show that BIC and $\phi(p, 0)$ are weakly consistent. For the AIC, we prove that the asymptotic distribution given by Shibata (1976) for the stationary autoregressive models continues to…

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The Order of Differencing in ARIMA Models

ARIMA 模型的差分阶数

A Lagrange multiplier test is derived for testing for the order of differencing in an autoregressive integrated moving average (ARIMA) model. The procedure is illustrated with an example.

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Measures of Conditional Linear Dependence and Feedback between Time Series

时间序列之间条件线性依赖与反馈的度量

Measures of linear dependence and feedback for two multiple time series conditional on a third are defined. The measure of conditional linear dependence is the sum of linear feedback from the first to the second conditional on the third, linear feedback from the second to the first conditional on the third, and instantaneous linear feedback between the first and second series conditional on the third. The measures are non-negative and may be expressed in terms of measures of…

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A Note on Kalman Filtering for the Seasonal Moving Average Model

季节移动平均模型的卡尔曼滤波注记

We show that if we apply the Kalman filter to a pure seasonal moving average model with no missing observations, then, by using a result of Ansley (1979), we can obtain significant computational savings.

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Estimation of a Quarterly Macroeconomic Model with Quantity Rationing

带数量配给的季度宏观经济模型估计

We specify and estimate a small fix-price model with quantity rationing on both the goods and labor markets. The side of the market which is rationed is random. The model is able to generate a productivity cycle and the degree of capacity utilization is endogenous. The rationing scheme, allocating supply between the various components of demand is estimated. The probabilities of being in the various regimes, the intensity of the disequilibrium on the markets, and the results…

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A Note on Using State-Dependent Models With a Time-Dependent Variance

具有时变方差的状态依赖模型使用札记

This research presents an extension of the state-dependent models (SDM) developed by Priestley. For some series, improvement in SDM performance may be achieved by permitting the residual variance to vary through time according to a moving-average scheme.

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Unobserved-Components Models for Seasonal Adjustment Filters

季节调整滤波器的不可观测成分模型

Time series models are presented, for which the seasonal-component estimates delivered by linear least squares signal extraction closely approximate those of the standard option of the widely-used Census X-11 program. Earlier work is extended by consideration of a broader class of models and by examination of asymmetric filters, in addition to the symmetric filter implicit in the adjustment of historical data. Various criteria that guide the specification of unobserved-…

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Issues Involved With the Seasonal Adjustment of Economic Time Series

经济时间序列季节调整中的问题

In the first part of this article, we briefly review the history of seasonal adjustment and statistical time series analysis in order to understand why seasonal adjustment methods have evolved into their present form. This review provides insight into some of the problems that must be addressed by seasonal adjustment procedures and points out that advances in modern time series analysis raise the question of whether seasonal adjustment should be performed at all. This in…

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[Issues Involved with the Seasonal Adjustment of Economic Time Series]: Comment

《经济时间序列季节调整涉及的问题》评论

Estela Bee Dagum, Normand J. D. Laniel, [Issues Involved with the Seasonal Adjustment of Economic Time Series]: Comment, Journal of Business & Economic Statistics, Vol. 2, No. 4 (Oct., 1984), pp. 328-332

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[Issues Involved with the Seasonal Adjustment of Economic Time Series]: Comment: On Dips in the Spectrum of a Seasonally Adjusted Time Series

《经济时间序列季节调整涉及的问题》评论:季调序列频谱中的凹陷

Craig F. Ansley, William E. Wecker, [Issues Involved with the Seasonal Adjustment of Economic Time Series]: Comment: On Dips in the Spectrum of a Seasonally Adjusted Time Series, Journal of Business & Economic Statistics, Vol. 2, No. 4 (Oct., 1984), pp. 323-324

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An Asymptotic Expansion Associated with the Maximum Likelihood Estimators in Arma Models

ARMA 模型极大似然估计量的渐近展开

SUMMARY A technique is given for the Edgeworth type asymptotic expansion for the joint as well as marginal and conditional distributions of the maximum likelihood estimators in autoregressive moving-average (ARMA) models. Our methodology is illustrated and results on the expansions for some simple ARMA models are presented.

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Infinitesimal Robustness for Autoregressive Processes

自回归过程的无穷小稳健性

We define the influence function and construct optimal robust estimators for autoregressive processes. We show that the asymptotic bias caused by small contaminations of the marginals can be written as the integral of a certain function with respect to the contamination. This function is called the influence function. It is unique only up to an equivalence relation, but there is a natural unique version which describes the limiting influence of an additional observation…

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On Bootstrapping Two-Stage Least-Squares Estimates in Stationary Linear Models

平稳线性模型中两阶段最小二乘估计的自助法

For models similar to those used in econometric work, under suitable regularity conditions, the bootstrap is shown to give asymptotically valid approximations to the distribution of errors in coefficient estimates.

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The G-Spectral Estimator

G谱估计量

In this article a modified definition of the G-spectral estimator is given. It is shown that the resulting estimator is a method of moments autoregressive moving average (ARMA) spectral estimator that does not require an estimate of the moving average parameters. As a result, a new formula for the power spectrum of an ARMA process is given that does not explicitly involve the moving average (MA) parameters. This formula then leads to a closed-form expression for the MA…

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A Method for Autoregressive-Moving Average Estimation

自回归移动平均模型的一种估计方法

The problem considered is that of estimating an autoregressive-moving average system, including estimating the degrees of the autoregressive and moving average lag operators. The basic method is that introduced by Hannan & Rissanen (1982). However, that method may sometimes overestimate the degrees and modifications are here introduced to correct this. The problem is itself due to the use of a long autoregression, of order clogT when T is large, in the first stage of the…

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Parameter Inference for a Nearly Nonstationary First-Order Autoregressive Model

近非平稳一阶自回归模型的参数推断

The finite sample behaviour of the score function in a first-order autoregression is investigated. An object is to interpret the transition of the distribution of the score when the model approaches a nonstationary situation with a unit root. A framework is presented wherein the nonnormality of the score is clearly seen. Also, a simple interpretation for the behaviour of the distribution in terms of two chi-squared variables is given. Approximate finite sample distributions…

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Local Asymptotic Specification Error Analysis

局部渐近设定误差分析

An approximation to the inconsistency introduced by imposing an incorrect restriction on a parametric model is given. The approximation can be applied to estimators generated by optimizing any objective function satisfying certain regularity conditions. Examples given include analysis of misspecification in discrete choice and time-series models estimated by maximum likelihood, and in a nonlinear regression model. SPECIFICATION ERROR ANALYSIS in the linear regression model…

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Distributions of the Sample Autocorrelations When Observations Are From a Stationary Autoregressive-Moving-Average Process

平稳自回归移动平均过程下样本自相关系数的分布

This article examines the adequacy of approximations to the distributions of the sample autocorrelations by normal distributions, Edgeworth-type expansions, and four-parameter Pearson distributions. The accuracy of these approximations is found to depend critically on the data-generating process and sample size and to improve with sample size. Only the Pearson approximations seem to be reliable in relatively small samples. The utility of these approximations is illustrated…

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Seasonal Adjustment of the Weekly Monetary Aggregates: A Model-Based Approach

周度货币总量的季节调整:基于模型的方法

A procedure is developed for seasonally adjusting weekly time series, based on a composite of regression and time series models. The procedure is applied to some weekly U.S. money supply series currently seasonally adjusted by the Federal Reserve.

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A Comparison of Autoregressive Univariate Forecasting Procedures for Macroeconomic Time Series

宏观时间序列单变量自回归预测程序的比较

The actual performance of several automated univariate autoregressive forecasting procedures, applied to 150 macroeconomic time series, are compared. The procedures are the random walk model as a basis for comparison; long autoregressions, with three alternative rules for lag length selection; and a long autoregression estimated by minimizing the sum of absolute deviations. The sensitivity of each procedure to preliminary transformations, data, periodicity, forecast horizon,…

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