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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…

圆周数据的时间序列分析AI 解读

SUMMARY The paper considers the problem of modelling and analysing a time series of measurements which take the form of unit two-dimensional vectors. Several general classes of existing and new models are studied in terms of feasibility and flexibility. An approach is recommended which uses two of these classes, and which takes advantage of several standard time series algorithms that are available in modern software packages. An application is given to the analysis of a…

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单变量季节时间序列建模的多变量方法AI 解读

A seasonal time series can be represented by a vector autoregressive model for the annual series containing the seasonal observations. This model allows for periodically varying coefficients. When the vector elements are integrated, the maximum likelihood cointegration method can be used to check for the presence of, possibly restricted, cointegration relations between these annual series. In this paper it is shown that this application generalizes a test procedure for…

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长期与短期结构的识别：ISLM 模型应用AI 解读

In this paper we discuss the problem of identification in a model with cointegration. It is pointed out that there is an identification problem for both long-run parameters and short-run parameters. The identification of the equations and the cointegrating relations is achieved by linear restrictions on the parameters and a criterion for a statistical model to be identifying is given. We also define empirical identification of an estimated structure. A switching algorithm…

商业周期的周期性结构AI 解读

This article tests whether an economic recovery is equally likely to occur in any month of the year. I test this hypothesis with a homogeneous Markov switching-regime model and use the turning-point dates for business cycles marked by the National Bureau of Economic Research and Romer. I tend to find equal probabilities to switch from recession to expansions. In particular, the spring and the month of December appear to have higher incidence of economic recovery. My results…

将潜在产出作为潜变量进行估计AI 解读

This article proposes a new method for estimating potential output in which potential real gross domestic product (GDP) is modeled as an unobserved stochastic trend and deviations of GDP from potential affect inflation through an aggregate supply relationship. The output and inflation equations together form a bivariate unobserved-components model that is estimated via maximum likelihood through the use of the Kalman-filter algorithm. The procedure yields a measure of…

线性二次模型中的协整检验AI 解读

This article evaluates the finite-sample performance of various tests for cointegration by Monte Carlo methods. The evaluation takes place within the linear quadratic model. The results indicate sharp differences in the ability of the tests to detect cointegrating relations, especially when the cost-of-adjustment term and the number of regressors are large. Although no single test dominates for all the parameter settings considered, overall the augmented Dickey-Fuller,…

经济周期阶段及其转移动态AI 解读

This article examines differences in expansionary and contractionary phases of the business cycle. By extending the nonlinear Markov-switching estimation method of J. D. Hamilton to incorporate time-varying probabilities of transitions between the phases, the marginal benefits of the time-varying transition probability Markov-switching model are highlighted. Using this technique, the author documents the high correlation between the evolution of the phases inferred from the…

重尾观测噪声下的稳健递归估计AI 解读

Under the usual assumptions of normality, the recursive estimator known as the Kalman filter gives excellent results and has found an extremely broad field of application--not only for estimating the state of a stochastic dynamic system, but also for estimating model parameters as well as detecting abrupt changes in the states or the parameters. It is well known, however, that significantly nonnormal noise, and particularly the presence of outliers, severely degrades the…

平稳序列经验过程的分块 BootstrapAI 解读

We apply the bootstrap for general stationary observations, proposed by Kunsch, to the empirical process for $p$-dimensional random vectors. It is known that the empirical process in the multivariate case converges weakly to a certain Gaussian process. We show that the bootstrapped empirical process converges weakly to the same Gaussian process almost surely, assuming that the block length $l$ for constructing bootstrap replicates satisfies $l(n) = O(n^{1/2-\varepsilon}), 0 < \varepsilon < \frac{1}{2}$…

平稳观测经验过程的分块自助法有效性AI 解读

We show that the empirical process of the block-based bootstrap observations from a stationary sequence converges weakly to an appropriate Gaussian process, conditionally in probability and almost surely, depending upon the block length. This bootstrap was introduced by Kunsch and later by Liu and Singh. Applications in estimation of the sampling distribution of a compactly differentiable functional are indicated.

分布变化检测的高效序贯非参数方案AI 解读

Suppose that a system in its standard state produces i.i.d. observations whose distribution is symmetric about zero. At an unknown time the system may leave its standard state, and the observations would subsequently be stochastically larger. Subject to a bound on the rate of false alarms, one wants to detect quickly such a departure from the standard state. We present a robust method of detection which is computationally feasible and remarkably efficient. The method is…