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在未知平稳化方式下建模股票价格AI 解读

Bayesian procedures for evaluating linear restrictions imposed by economic theory on dynamic econometric models are applied to a simple class of presentvalue models of stock prices. The procedures generate inferences that are not conditional on ancillary assumptions regarding the nature of the nonstationarity that characterizes the data. Inferences are influenced by prior views concerning nonstationarity, but these views are formally incorporated into the analysis, and…

解释变量单整阶数未知时的时间序列回归推断AI 解读

The distribution of statistics testing restrictions on the coefficients in time series regressions can depend on the order of integration of the regressors. In practice, the order of integration is rarely known. We examine two conventional approaches to this problem — simply to ignore unit root problems or to use unit root pretests to determine the critical values for second-stage inference—and show that both exhibit substantial size distortions in empirically plausible…

宏观经济学家应了解的单位根问题：贝叶斯视角AI 解读

This paper summarizes recent Bayesian research on unit roots for the applied macroeconomist in the way Campbell and Perron [8] summarized the classical unit roots perspective. The appropriate choice of a prior is discussed. In recognizing a consensus distaste for explosive roots, I find the popular Normal-Wishart priors centered at the unit root to be reasonable provided they are modified by concentrating the prior mass for the time trend coefficient toward zero as the…

使用精确似然函数时的 Jeffreys 先验AI 解读

In this paper, we calculate Jeffreys prior for an AR(1) process with and without a constant and a time trend when using the exact likelihood function. We show how this prior can be calculated for the explosive region, even though the unconditional variance of the process is infinite. The calculations lend additional support to the Schotman-van Dijk [6] procedure for restricting the location and the variance of the time trend coefficient. The results show that flat priors are…

趋势平稳与差分平稳的贝叶斯推断AI 解读

This paper proposes a general Bayesian framework for distinguishing between trend- and difference-stationarity. Usually, in model selection, we assume that all of the data were generated by one of the models under consideration. In studying time series, however, we may be concerned that the process is changing over time, so that the preferred model changes over time as well. To handle this possibility, we compute the posterior probabilities of the competing models for each…

不可观测成分模型中的单位根假设：贝叶斯分析AI 解读

In this paper we extend some of Phillips's [4] results to nonlinear unobserved components models and develop a posterior odds ratio test of the unit root hypothesis based on flat and Jeffreys priors. In contrast to the analysis presented by Schotman and van Dijk [9], we utilize a nondegenerate structural representation of the components model that allows us to determine well-behaved Jeffreys priors, posterior densities under flat priors and Jeffreys priors, and posterior…

经济时间序列的贝叶斯预测AI 解读

A model is suggested to forecast economic time series. This model incorporates some innovative ideas of Harrison and Stevens [20] for building into the forecasting process important external shocks to the systems. Thus the occurrence of possibly significant real-world events may cause a fundamental change in the time series in question. The Jeffreys-Savage (JS) Bayesian theory of hypothesis testing is used to test the hypothesis that a particular event has been such as to…

AR(1) 模型的无信息先验与贝叶斯检验AI 解读

Various approaches to the development of a noninformative prior for the AR(1) model are considered and compared. Particular attention is given to the reference prior approach, which seems to work well for the stationary case but encounters difficulties in the explosive case. A symmetrized (proper) version of the stationary reference prior is ultimately recommended for the problem. Bayesian testing of the unit root, stationary, and explosive hypotheses is considered also.…

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宏观经济时间序列的先验及其应用AI 解读

This paper takes up Bayesian inference in a general trend stationary model for macroeconomic time series with independent Student- t disturbances. The model is linear in the data, but nonlinear in parameters. An informative but nonconjugate family of prior distributions for the parameters is introduced, indexed by a single parameter that can be readily elicited. The main technical contribution is the construction of posterior moments, densities, and odd ratios by using a…

AR(1) 模型的先验：参数化问题与时间序列考量AI 解读

Two issues have come up in the specification of a prior in the Bayesian analysis of time series with possible unit roots. The first issue deals with the singularity that is due to the local identification problem of the unconditional mean of an AR(1) process in the limit of a random walk. This singularity problem is related to the difference between a structural parameterization and the linear reduced form in a standard regression model with fixed regressors. The second is…

协整模型中似然与后验的形状AI 解读

A vector autoregressive (VAR) model is specified with equation system parameters, which directly reflect the possible cointegrating nature of the analyzed time series. By using a flat/diffuse prior, we show that the marginal posteriors of the parameters of interest (multipliers of the cointegrating vectors) may be nonintegrable and favor difference stationary models in an undesired way. To choose between stationary, cointegrated, and difference stationary models in a…

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Solution: Econometric Theory, 10, n. 2, june 1994 p. 449, erratum Econometric Theory 11, n. 2, p. 402.

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GLM 用于设定检验的局限：对 Gurmu 与 Trivedi 的评论AI 解读

In this comment on Gurmu and Trivedi's “Variable Augmentation Specification Tests in the Linear Exponential Family,” I show how their generalized linear model (GLM) approach relates to other work in econometrics on specification testing in the linear exponential family. In addition to shedding light on the relationship between the statistics and econometrics literatures on testing in quasi-likelihood frameworks, this comparison reveals some important limitations of GLM as a…