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弱 VARMA 过程的实用建模：识别、估计、模型设定与宏观应用AI 解读

We consider the problem of developing practical methods for modelling weak VARMA processes. We first propose new identified VARMA representations, the diagonal MA equation form and the final MA equation form, where the MA operator is either diagonal or scalar. Both these representations have the important feature that they constitute relatively simple modifications of a VAR model (in contrast with the echelon representation). Second, for estimating VARMA models, we develop…

因子增强 VARMA 模型及其宏观经济应用AI 解读

We study the relationship between vector autoregressive moving-average (VARMA) and factor representations of a vector stochastic process. We observe that, in general, vector time series and factors cannot both follow finite-order VAR models. Instead, a VAR factor dynamics induces a VARMA process, while a VAR process entails VARMA factors. We propose to combine factor and VARMA modeling by using factor-augmented VARMA (FAVARMA) models. This approach is applied to forecasting…

短期与长期因果度量：理论与推断AI 解读

The concept of causality introduced by Wiener [Wiener, N., 1956. The theory of prediction, In: E.F. Beckenback, ed., The Theory of Prediction, McGraw-Hill, New York (Chapter 8)] and Granger [Granger, C. W.J., 1969. Investigating causal relations by econometric models and cross-spectral methods, Econometrica 37, 424-459] is defined in terms of predictability one period ahead. This concept can be generalized by considering causality at any given horizon h as well as tests for…

未知异方差与非线性依赖下线性中位数回归的有限样本无分布推断AI 解读

We construct finite-sample distribution-free tests and confidence sets for the parameters of a linear median regression, where no parametric assumption is imposed on the noise distribution. The set-up studied allows for non-normality, heteroscedasticity, non-linear serial dependence of unknown forms as well as for discrete distributions. We consider a mediangale structure--the median-based analogue of a martingale difference--and show that the signs of mediangale sequences…

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马尔可夫过程、双向自回归与平稳及非平稳自回归的有限样本推断AI 解读

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression…

时间序列中的短期与长期因果性：理论AI 解读

Causality in Granger's sense is defined in terms of predictibility one period ahead. The notion of causality is generalized by considering causality at any given horizon 1 <= h <= inifinity, providing a rigorous formalization of indirect causal effects and causality chains in (possibly) nonstationary time series. The authors derive necessary and sufficient conditions for noncausality between vectors up to any given horizon. They observe that coefficients of lagged variables…

一阶自回归分布滞后模型的精确推断方法AI 解读

Exact tests and confidence sets are obtained for general transformations of the coefficients in linear first-order autoregressive models with exogenous variables and i.i.d. disturbances. The tests proposed have known level and are either similar (constant rejection probability under all processes consistent with the null hypothesis) or use bounds which are free of nuisance parameters. Correspondingly, the confidence sets are either similar with known size or conservative.…

计量经济学中的若干不可能性定理及其在结构与动态模型中的应用AI 解读

General characterizations of valid confidence sets and tests in problems involving (locally almost) unidentified (LAU) parameters are presented. In particular, any valid confidence set for an unbounded LAU parameter must be unbounded with positive probability. Consequently, almost surely bounded confidence sets, like Wald-type confidence sets, have zero coverage probability and Wald-type test statistics cannot be pivotal functions. The results are applied to simultaneous…

多元ARMA模型中两个变量向量之间的因果性检验AI 解读

In the analysis of economic time series, a question often raised is whether a vector of variables causes another one in the sense of Granger. Most of the literature on this topic is concerned with bivariate relationships or uses finite-order autoregressive specifications. The purpose of this article is to develop a causality analysis in the sense of Granger for general vector autoregressive moving average (ARMA) models. We give a definition of Granger noncausality between…

误差自相关线性回归中的精确检验与置信集AI 解读

This article proposes a general method to build exact tests and confidence sets in linear regressions with first-order autoregressive Gaussian disturbances. Because of a nuisance parameter problem, we argue that generalized bounds tests and conservative confidence sets provide natural inference procedures in such a context. Given an exact confidence set for the autocorrelation coefficient, we describe how to obtain a similar simultaneous confidence set for the…

估计向量自回归模型预测的无偏性AI 解读

Forecasts from a univariate autoregressive model estimated by OLS are unbiased, irrespective of whether the model fitted has the correct order; this property only requires symmetry of the distribution of the innovations. In this paper, this result is generalized to vector autoregressions and a wide class of multivariate stochastic processes (which include Gaussian stationary multivariate stochastic processes) is described for which unbiasedness of predictions holds:…