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二阶单整向量自回归过程的表示AI 解读

We investigate vector autoregressive processes and find the condition under which the processes are I (2). A representation theorem forsuch processes is proved and the interpretation of the AR model as an error correction model is discussed.

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随机微分方程系统的连续记录渐近理论AI 解读

This paper considers estimation based on a set of T + 1 discrete observations, y (0), y ( h ), y (2 h ),…, y ( Th ) = y ( N ), where h is the sampling frequency and N is the span of the data. In contrast to the standard approach of driving N to infinity for a fixed sampling frequency, the current paper follows Phillips [35,36] and Perron [29] and examines the “dual” asymptotics implied by letting h tend to zero while the span N remains fixed. We suggest a way of explicitly…

通过自回归近似估计与检验协整系统AI 解读

This paper studies the estimation and testing of general cointegrated systems by using an autoregressive approximation. Simple estimators for both the cointegration vectors and their weight matrix in the autoregressive error correction model representation of the system are developed. Since these estimators assume that the number of cointegration vectors and their normalization are fixed in advance, convenient specification tests for checking the validity of these…

典范协整回归AI 解读

A new procedure for statistical inference in cointegrating regressions is developed. The author introduces canonical cointegrating regressions (regressions formulated with the transformed data). The required transformations involve simple adjustments of the integrated processes using stationary components in cointegrating models. Canonical cointegrating regressions, therefore, represent the same cointegrating relationships as the original models. They are, however,…

“客观”贝叶斯单位根检验AI 解读

Abstract Due to weaknesses in traditional tests, a Bayesian approach is developed to investigate whether unit roots exist in macroeconomic time‐series. Bayesian posterior odds comparing unit root models to stationary and trend‐stationary alternatives are calculated using informative priors. Two classes of reference priors which are informative but require minimal subjective prior input are used. In this sense the Bayesian unit root tests developed here are objective.…

存在漂移时单位根的插值检验AI 解读

This paper considers tests of the null hypothesis of a unit root in an observed time series against the alternative that the series is level stationary. Interpolation tests whose critical values depend upon the value of the drift parameter are compared to the standard Dickey-Fuller tests in Monte Carlo simulations. The interpolation test performs quite well especially against one-sided alternatives.

高斯向量自回归模型中协整向量的估计与假设检验AI 解读

This paper contains the likelihood analysis of vector autoregressive models allowing for cointegration. The author derives the likelihood ratio test for cointegrating rank and finds it asymptotic distribution. He shows that the maximum likelihood estimator of the cointegrating relations can be found by reduced rank regression and derives the likelihood ratio test of structural hypotheses about these relations. The author shows that the asymptotic distribution of the maximum…

贝叶斯路径与单位根：先验问题始终值得争论AI 解读

Abstract This paper provides detailed responses to the following eight discussants of my paper ‘To criticize the critics: an objective Bayesian analysis of stochastic trends’: Gary Koop and Mark Steel; Edward Learner; In‐Moo Kim and G. S. Maddala; Dale J. Poirier; Peter C. Schotman and Herman K. van Dijk; James H. Stock; David DeJong and Charles H. Whiteman; and Christopher Sims. This reply puts new emphasis on the call made in the earlier paper for objective Bayesian…

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批评批评者：随机趋势的客观贝叶斯分析AI 解读

Abstract In two recent articles, Sims (1988) and Sims and Uhlig (1988/1991) question the value of much of the ongoing literature on unit roots and stochastic trends. They characterize the seeds of this literature as ‘sterile ideas’, the application of nonstationary limit theory as ‘wrongheaded and unenlightening’, and the use of classical methods of inference as ‘unreasonable’ and ‘logically unsound’. They advocate in place of classical methods an explicit Bayesian approach…

单位根贝叶斯推断的不同路径AI 解读

Abstract This paper is a comment on P. C. B. Phillips, ‘To criticise the critics: an objective Bayesian analysis of stochastic trends’ [Phillips, (1991)]. Departing from the likelihood of an univariate autoregressive model different routes that lead to a posterior odds analysis of the unit root hypothesis are explored, where the differences in routes are due to the different choices of the prior. Improper priors like the uniform and the Jeffreys prior are less suited for…

采样频率变化下的检验一致性AI 解读

This paper considers the consistency property of some test statistics based on a time series of data. While the usual consistency criterion is based on keeping the sampling interval fixed, we let the sampling interval take any equispaced path as the sample size increases to infinity. We consider tests of the null hypotheses of the random walk and randomness against positive autocorrelation (stationary or explosive). We show that tests of the unit root hypothesis based on the…

连续时间中的误差修正与长期均衡AI 解读

This paper deals with error correction models (ECM's) and cointegrated systems that are formulated in continuous time. Long-run equilibrium coefficients in the continuous system are always identified in the discrete time reduced form, so that there is no aliasing problem for these parameters. The long- run relationships are also preserved under quite general data filtering. Frequency domain procedures are outlined for estimation and inference. These methods are…

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现值关系中的协整检验AI 解读

A Bayesian methodology is used to examine the bivariate time series properties of stock prices and dividends. The hypothesis that stock prices and dividends are cointegrated is emphasized. Exact small sample results are calculated using a specific parameterization for the bivariate model. Some commonly encountered problems in conventional cointegration tests based on asymptotic theory are thereby eliminated. We consider three hypotheses whose nonlinear form entails the need…

季节差分的若干拉格朗日乘子检验AI 解读

Determining whether a time series has a unit root is an important problem in many time series analyses. For seasonal time series the problem is more complicated as one has to decide whether both regular and seasonal differencing or just one of them would suffice to transform a series into stationarity. This important problem is addressed via the Lagrange multiplier test approach. The large sample representations of the test statistics in terms of integrals of Wiener…

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一阶自回归预测的偏差AI 解读

The exact finite sample behavior is investigated on the bias of multiperiod leastsquares forecasts in the normal autoregressive model y t = α + β y t –1 + u t . Necessary and sufficient conditions are given for the existence of the bias and an expression is presented which we use to obtain exact numerical results for finite samples. The unit root and near unit root behavior is studied in detail and some popular preconceptions about the behavior of the bias are shown to be…

新古典宏观框架下名义货币与实际产出的贝叶斯分析AI 解读

This study investigates the empirical evidence on the effects of unanticipated changes in nominal money on real output in 47 countries when viewed through a window (i.e., likelihood function) that assumes the neutrality of anticipated changes. Using a Bayesian predictivist approach, it provides a pedagogical Bayesian analysis of generated regressor models in the face of specification uncertainty involving, among other things, multiple unit root and trend stationary…

协整系统中的最优推断AI 解读

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…

协整回归的渐近有效估计AI 解读

An asymptotic optimality theory for the estimation of cointegration regressions is developed in this paper. The theory applies to a reasonably wide class of estimators without making any specific assumptions about the probability distribution or short-run dynamics of the data-generating process. Due to the nonstandard nature of the estimation problem, the conventional minimum variance criterion does not provide a convenient measure of asymptotic efficiency. An alternative…