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Optimal Inference in Cointegrated Systems

协整系统中的最优推断

Properties of maximum likelihood estimates of cointegrated systems are studied. Alternative formulations are considered, including a new triangular system error correction mechanism. We demonstrate that full system maximum likelihood brings the problem of inference within the family covered by the locally asymptotically mixed normal asymptotic theory, provided all unit roots have been eliminated by specification and data transformation. Methodological issues provide a major…

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A Comparison of the Forecasting Ability of ECM and VAR Models

The results of forecasting experiments based on an error correction mechanism (ECM) model and various types of vector autoregressive (VAR) and Bayesian vector autoregressive (BVAR) models are presented. A Bayesian error correction mechanism (BECM) model is also tested. This model represents a hybrid of the BVAR and ECM models. The results from experiments using fifty industries and monthly Ohio labor market data demonstrate that the ECM model produces forecasts with much…

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Canonical Correlation in Multivariate Time Series Analysis With an Application to One-Year-Ahead and Multiyear-Ahead Macroeconomic Forecasting

A simple one-period-ahead and multiperiod-ahead prediction procedure for multivariate time series is suggested, based on the canonical correlation technique. The prediction procedure is direct in the sense that no lag orders and parameters have to be estimated first, as in the usual ARMAX or VAR parameterizations of multivariate stationary stochastic processes. A best (in the mean squared error sense) predictor can be obtained directly using singular-value decompositions of…

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From a var model to a structural model, with an application to the wage–price spiral

从 VAR 模型到结构模型:工资—价格螺旋的应用

Abstract In this paper a VAR model is considered as a general framework in which a structural model can be tested. We carefully describe the hypotheses defining a structural model; this leads us to discuss various notions such as: predeterminedness, non‐causality, exogeneity, contemporaneous identification, overall identification, weak and strong structural forms. Then we propose a test procedure, based on the asymptotic least‐squares method, which allows successive testing…

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Asymptotic Properties of Multivariate Nonstationary Processes with Applications to Autoregressions

多元非平稳过程的渐近性质及其自回归应用

Asymptotic properties of multivariate time series with characteristic roots on the unit circle are considered. For a vector autoregressive moving average (ARMA) process, we derive the limiting distributions of certain statistics which are useful in understanding nonstationary processes. These distributions are derived in a unified manner for all types of characteristic roots and are expressed in terms of stochastic integrals of Brownian motions. For applications, we use the…

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Asymptotic Expansions of the Distributions of Statistics Related to the Spectral Density Matrix in Multivariate Time Series and Their Applications

多元时间序列谱密度矩阵相关统计量的分布渐近展开及应用

Let { X ( t )} be a multivariate Gaussian stationary process with the spectral density matrix f 0 (ω), where θ is an unknown parameter vector. Using a quasi-maximum likelihood estimator θ̂ of θ, we estimate the spectral density matrix f 0 (ω) by f θ̂ (ω). Then we derive asymptotic expansions of the distributions of functions of f θ̂ (ω). Also asymptotic expansions for the distributions of functions of the eigenvalues of f θ̂ (ω) are given. These results can be applied to…

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Asymptotic Distributions of Impulse Response Functions and Forecast Error Variance Decompositions of Vector Autoregressive Models

向量自回归模型中脉冲响应函数与预测误差方差分解的渐近分布

In recent years, vector autoregressive models have become standard tools for economic analyses. Impulse response functions and forecast error variance decompositions are usually computed from these models in order to investigate the interrelationships within the system. However, sometimes no measures of estimation uncertainty are provided by authors. One reason may be that the relevant asymptotic distribution theory is distributed over various publications. In this article,…

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Inference in Linear Time Series Models with some Unit Roots

含部分单位根的线性时间序列模型中的推断

This paper considers estimation and hypothesis testing in linear time series when some or all of the variables have (possibly multiple) unit roots. The motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as regressors. Parameters that can be written as coefficients on mean zero, nonintegrated regressors have jointly normal asymptotic distribution, converging at the rate of T(superscript…

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Parsimonious Parameterization of Vector Autoregressive Moving Average Models

向量自回归移动平均模型的简约参数化

It is not uncommon to hear the complaint that there are many difficulties in building vector autoregressive moving average (ARMA) models, such as too many parameters in a model. In this article, I show that the complaint can be avoided if a proper method is used at the model-specification stage to obtain the detailed structure of the vector process under study. Two such methods, one from the engineering literature and the other from the statistical literature, are discussed.…

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Statistical Inference in Regressions with Integrated Processes: Part 2

含单整过程回归的统计推断:第二部分

This paper continues the theoretical investigation of Park and Phillips. We develop an asymptotic theory of regression for multivariate linear models that accommodates integrated processes of different orders, nonzero means, drifts, time trends, and cointegrated regressors. The framework of analysis is general but has a common architecture that helps to simplify and codify what would otherwise be a myriad of isolated results. A good deal of earlier research by the authors…

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Model Specification in Multivariate Time Series

多元时间序列的模型设定

SUMMARY We propose a method to specify an appropriate yet parsimonious vector autoregressive moving average (ARMA) model for a given multivariate time series. By considering contemporaneous linear transformations of the vector process, we introduce the concept of scalar component models within the vector ARMA framework (a) to reveal possibly hidden simplifying structures of the process, (b) to achieve parsimony in parameterization and (c) to identify the exchangeable models.…

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Testing for Common Trends

共同趋势检验

Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix obtained by regressing the series onto its first lag. Critical values for the tests are tabulated, and their power is examined in a Monte Carlo study. Economic time series are…

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Nonparametric Time-Series Estimation of Joint DGP, and Vector Autoregression (Econometric Theory 1 (1985): 27–52)

《联合数据生成过程的非参数时间序列估计与向量自回归》证明问题说明

Several problems with the proofs of Theorems 2, 3, and 4 given in the above article were drawn to our attention by Professor P. M. Robinson. A complete and rigorous set of conditions under which the main results of these theorems hold has not been found yet.

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Statistical Inference in Regressions with Integrated Processes: Part 1

含单整过程回归的统计推断:第一部分

This paper develops a multivariate regression theory for integrated processes which simplifies and extends much earlier work. Our framework allows for both stochastic and certain deterministic regressors, vector autoregressions, and regressors with drift. The main focus of the paper is statistical inference. The presence of nuisance parameters in the asymptotic distributions of regression F tests is explored and new transformations are introduced to deal with these…

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Estimating Vector Autoregressions with Panel Data

利用面板数据估计向量自回归模型

This paper considers estimation and testing of vector autoregressio n coefficients in panel data, and applies the techniques to analyze the dynamic relationships between wages an d hours worked in two samples of American males. The model allows for nonstationary individual effects and is estimated by applying instrumental variables to the quasi-differenced autoregressive equations. The empirical results suggest the absence of lagged hours in the wage forecasting equation.…

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Asymptotic Distribution of the Moving Average Coefficients of an Estimated Vector Autoregressive Process

估计向量自回归过程的移动平均系数的渐近分布

The coefficients of the moving average (MA) representation of a vector autoregressive (VAR) process are the dynamic multipliers of the system. These quantities are often used to analyze the relationships between the variables involved. Assuming that the actual data generation process is stationary and has a VAR representation of unknown and possibly infinite order, the asymptotic distribution of the MA coefficients is derived. A computationally simple formula for the…

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An Econometric Analysis of Fluctuations in Aggregate Labor Supply and Demand

总量劳动供给与需求波动的计量分析

This paper contains an equilibrium model of the labor market. The supply function allows f or temporal substitution in response to wage fluctuations, and the de mand function allows for adjustment costs. Two related issues are emp hasized: identification of supply and demand functions, and sources o f serial correlation in employment and real wages. When the supply an d demand shocks are AR(1) processes, the equilibrium process for empl oyment and real wages is a restricted…

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Vector Autoregressions and Reality

向量自回归与现实

This article questions the statistical significance of variance decompositions and impulse response functions for unrestricted vector auto regressions. It suggests that previous authors have failed to provide confidence intervals for variance decompositions and impulse response functions. Two methods of computing such confidence intervals are developed: first, using a normal approximation; second, using bootstrapped resampling. An example from Sims's work is used to…

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Identification of Nonzero Elements in the Polynomial Matrices of Mixed Varma Processes

SUMMARY The parameter density is the polynomial matrices of vector autoregressive moving average (VARMA) time series models is generally very low. Thus, estimation of fully parameterized high order models or of models with many variables is an ineffective, if not impractical, way of utilizing computing power. In the article we present methods for identifying the nonzero elements in VARMA(1,1) models, and show how these procedures can be used to construct models of higher…

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Forecasting Wheat Exports: Do Exchange Rates Matter?

预测小麦出口:汇率是否重要?

A vector autoregression is fit to recent U.S. data on wheat prices, wheat export sales, wheat export shipments, and exchange rates. Forecast error decompositions and out-of-sample forecasts indicate that exchange rates have little influence on wheat sales and shipments.

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Co-Integration and Error Correction: Representation, Estimation, and Testing

协整与误差修正:表示、估计与检验

The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples. If each element of a vector of time series x first achieves stationarity after differencing, but a linear combination a'x is already stationary, the time series x are said to be co-integrated with co-integrating vector a. There may be several such co-integrating vectors so that a…

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