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Tests for Equality between Sets of Coefficients in Two Linear Regressions under Heteroscedasticity

异方差下两个线性回归系数集合相等的检验

Structural shift is a common problem in a relationship dealing with time series data. Chow (1960) developed a test to detect such a shift under the assumption that observations both before and after the shift have the same variance. Structural shifts, however, often accompany changes in variance as well, and the Chow test is not robust to such changes. Two relatively robust tests are proposed and are found to be highly powerful.

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Errors in Variables and Seasonal Adjustment Procedures

变量测量误差与季节调整程序

Seasonal adjustment procedures attempt to estimate the sample realizations of an unobservable economic time series in the presence of both seasonal and irregular factors. In this article, we consider a factor that has not been considered explicitly in previous treatments of seasonal adjustment: measurement error. Because of the sample design used in the Current Population Survey, measurement error will not be a white-noise process, but instead it will be characterized by…

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A Time Series Model for Cohort Data

队列数据的时间序列模型

Many forms of behavior are both age and cohort dependent. An appropriate way of disentangling these two kinds of effects is to examine changes between successive cohorts. Data on recent cohorts are always incomplete. A univariate time series model is presented for projecting age- or duration-specific data of recent cohorts. The model is also capable of taking period effects into account. By way of illustration, the model is applied to Dutch marital fertility rates.

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Tests for Equality Between Sets of Coefficients in Two Linear Regressions Under Heteroscedasticity

异方差下两个线性回归系数集合的相等性检验

Structural shift is a common problem in a relationship dealing with time series data. Chow (1960) developed a test to detect such a shift under the assumption that observations both before and after the shift have the same variance. Structural shifts, however, often accompany changes in variance as well, and the Chow test is not robust to such changes. Two relatively robust tests are proposed and are found to be highly powerful.

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Advanced Econometrics: A Bridge to the Literature.

高级计量经济学:通向文献的桥梁

TOPICS IN LARGE SAMPLE THEORY AND APPROXIMATION METHODS. A Review of Asymptotic Distribution Theory and Maximum Likelihood Estimation. Methods of Approximating Distribution Functions, Density Functions, and Moments. TOPICS IN TIME SERIES ANALYSIS. An Introduction to Time Series Analysis. Identification, Estimation, and Prediction in Time Series Models. The Relationship Between Time Series Models and Econometric Models. TOPICS IN ESTIMATION UNDER A QUADRATIC LOSS CRITERION.…

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Use of Canonical Analysis in Time Series Model Identification

典型分析在时间序列模型识别中的应用

The second-order moment structure of time series models is used to derive a canonical analysis in time series modelling. Consistency properties of certain canonical correlations and the corresponding eigenvectors are shown. Based on these properties, a canonical correlation approach for tentative order determination in building autoregressive-moving average models is proposed. This approach can handle directly nonstationary as well as stationary processes and it also…

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Chi-Plots for Assessing Dependence

用于评估依赖关系的 χ 图

This paper presents a graphical method to be used, in conjunction with a scatterplot, to investigate possible association of two variates as manifested in a sample of bivariate measurements. The method is designed so that the plot is approximately horizontal under independence, and under various forms of association it produces corresponding characteristic patterns. Examples given include application to study of regression residuals, dependence of two spatial point…

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On the Rate of Convergence of the Innovation Representation of a Moving Average Process

移动平均过程新息表示的收敛速度

A moving average process of order q can be written as a linear combination of the (q+1) most recent innovations. We show that if the moving average polynomial has roots on the unit circle, then the coefficients of the innovations tend to the true moving average coefficients, the difference between the two being O (1/t), where t is the number of observations we consider. The results are extended to mixed autoregressive moving average models and multivariate models.

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A Diffusion Process and Its Applications to Detecting a Change in the Drift of Brownian Motion

扩散过程及其在检测布朗运动漂移变化中的应用

The classical cusum procedure of Page (1954) and a competitor suggested independently by Shiryayev (1963) and Roberts (1966) for detecting a change in distribution are systematically compared, when the change point v = 0 and when v is large. The specific model considered is that of detecting a change in the drift of Brownian motion, for which diffusion theory yields certain explicit results that seem impossible to compute in discrete time. The Shiryayev-Roberts process turns…

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Edgeworth Expansion for the OLS Estimator in a Time Series Regression Model

时间序列回归中 OLS 估计量的 Edgeworth 展开

In this paper we consider the situation in which ordinary least squares (OLS) is used to estimate an ARMA (1,1) model with one exogenous variable. Applying Edgeworth expansion techniques, we examine the misspecification errors and the approximate distributions of the OLS estimator. Extensive numerical studies were performed and selected results are shown graphically. In addition, a technical device is developed to calculate the Edgeworth coefficients.

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A Theory of Serial Correlation of Stochastic Taste Changers in Direct Utility Functions

直接效用函数中随机偏好变动的序列相关理论

Methods of maximum-likelihood search (eg., Hildreth-Lu) for single equations models with autocorrelated disturbances are not easily extended to the multi-equation systems encountered in econometric studies of consumer demand. The obstacle is the large dimension of the space of independent serial correlation coefficients to be partitioned and searched. This paper treats stochastic disturbance vectors in demand/expenditure systems as functions of random disturbances in…

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A Point Optimal Test for Moving Average Regression Disturbances

回归扰动移动平均相关的点最优检验

This paper reconsiders King's [12] locally optimal test procedure for first-order moving average disturbances in the linear regression model. It recommends two tests, one for problems involving positively correlated disturbances and one for negatively correlated disturbances. Both tests are most powerful invariant at a point in the alternative hypothesis parameter space that is determined by a function involving the sample size and the number of regressors. Selected bounds…

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Testing for Serial Correlation in Regression with Missing Observations

存在缺失观测时的回归序列相关检验

SUMMARY In order to test for serial correlation in residuals for static time series regression in the presence of missing data, the score principle is applied both to the likelihood conditional on the observation times, and to an unconditional form of likelihood. Asymptotic distributions of the test statistics are established, under both the null hypothesis of no serial correlation, and sequences of local, correlated, alternatives, enabling analytic comparison of efficiency.

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A Model for High-Order Markov Chains

一种高阶马尔可夫链模型

SUMMARY A model for Markov chains of order higher than one is introduced which involves only one additional parameter for each extra lag. Asymptotic properties and the autocorrelation structure are investigated. Three examples are given in which the model appears to model data more successfully than both the usual high-order Markov chain and the alternative models of Jacobs and Lewis (1978), Pegram (1980) and Logan (1981).

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Neglected Method of Separating Demand and Supply in Time Series Regression

时间序列回归中一种被忽视的供需分离方法

This article argues that in many markets, quantity is demand determined in the short run but price is supply determined, and that the dynamic restrictions between price and quantity implied by the model have been widely neglected in empirical research. Two examples illustrate our point—the demand and supply relationships between inflation and unemployment and between the terms of trade and the trade balance. In both, specifying quantity as a function of lagged prices in…

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Trends and Cycles in Macroeconomic Time Series

宏观经济时间序列中的趋势与周期

Two structural time series models for annual observations are constructed in terms of trend, cycle, and irregular components. The models are then estimated via the Kalman filter using data on five U.S. macroeconomic time series. The results provide some interesting insights into the dynamic structure of the series, particularly with respect to cyclical behavior. At the same time, they illustrate the development of a model selection strategy for structural time series models.

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Model Identification in Dynamic Regression (Distributed Lag) Models

动态回归(分布滞后)模型的识别

Dynamic regression models (also known as distributed lag models) are widely used in engineering for quality control and in economics for forecasting. In this article I propose a procedure for specifying such models in practice. The proposed procedure requires no prewhitening and can directly handle the nonstationary series. Furthermore, the procedure cross-validates prior beliefs about causal relationships between variables with empirical findings to ensure the suitability…

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Exploring an Ozone Spatial Time Series in the Frequency Domain

在频域中探索臭氧的空间时间序列

In 1974, atmospheric scientists (Molina and Rowland; Cicerone et al.) first postulated that man-made chemicals known as CFC's (e.g., freon) deplete the earth's ozone when released into the atmosphere. This article presents an exploratory data analysis (EDA) of a spatial time series of ozone measurements. Frequency domain techniques for the EDA are introduced and used to graphically display global, long-term trends relevant to the CFC issue. My intention is to illustrate the…

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Forecasting Interstate Migration with Limited Data: A Demographic-Economic Approach

有限数据下的州际迁移预测:人口—经济方法

"The limitations of available migration data preclude a time-series approach of modeling interstate migration [in the United States]. The method presented here combines aspects of the demographic and economic approaches to forecasting migration in a manner compatible with existing data. Migration rates are modeled to change in response to changes in economic conditions. When applied to resently constructed data on migration based on income tax returns and then compared to…

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Foreign-Exchange Rate Dynamics: An Empirical Study Using Maximum Entropy Spectral Analysis

外汇汇率动态:基于最大熵谱分析的实证研究

This study examines whether foreign-exchange rates evolve as a random walk by directly comparing the predictive ability of autoregressive (AR) models of spot rates with that of the random walk. To reduce the influence of model specifications on test results, we neither specify the order of the AR process a priori nor assume that the order is necessarily the same over the entire sample period. For each subperiod, the AR model is estimated by maximum entropy spectral analysis,…

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A Framework for Time Varying Parameter Regression Modeling

时变参数回归建模框架

A framework for time varying parameter regression models is developed and employed in modeling and forecasting price expectations, using the Livingston data. Alternative model formulations, which include various choices for both the stochastic processes generating the varying parameters and the sets of explanatory variables, are examined and compared by using this framework. These models, some of which have appeared elsewhere and some of which are new, are estimated and used…

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On the Optimal Use of Suboptimal Forecasts of Explanatory Variables

解释变量的次优预测如何得到最优利用

Ashley (1983) gave a simple condition for determining when a forecast of an explanatory variable (Xt ) is sufficiently inaccurate that direct replacement of Xt by the forecast yields worse forecasts of the dependent variable than does respecification of the equation to omit Xt . Many available macroeconomic forecasts were shown to be of limited usefulness in direct replacement. Direct replacement, however, is not optimal if the forecast's distribution is known. Here optimal…

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