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单位根过程的状态空间规范形式AI 解读

In this paper we develop a canonical state space representation of autoregressive moving average (ARMA) processes with unit roots with integer integration orders at arbitrary unit root frequencies. The developed representation utilizes a state process with a particularly simple dynamic structure, which in turn renders this representation highly suitable for unit root, cointegration, and polynomial cointegration analysis. We also propose a new definition of polynomial…

对持续性稳健的增广滞后 Granger 因果检验AI 解读

Previous literature has introduced causality tests with conventional limiting distributions in I(0)/I(1) vector autoregressive (VAR) models with unknown integration orders, based on an additional surplus lag in the specification of the estimated equation, which is not included in the tests. By extending this surplus lag approach to an infinite order VARX framework, we show that it can provide a highly persistence-robust Granger causality test that accommodates i.a…

含某些多频 I(1) 回归变量时 OLS 估计误差的几乎必然界AI 解读

Lai and Wei (1983, Annals of Statistics 10, 154–166) state in their Theorem 1 that the estimators of the regression coefficients in the regression $y_t = x_t^' \beta + \varepsilon _{\rm{t}} $ , t ∈ ℕ are almost surely (a.s.) consistent under the assumption that the minimum eigenvalue λ min ( T ) of $\sum\nolimits_{t = 1}^T {x_t } x'_t $ tends to infinity (a.s.) and log( λ max ( T ))/ λ min ( T ) → 0 (a.s.) where λ max ( T ) denotes the maximal eigenvalue.…

条件异方差创新下多元 ARMA 模型的子空间估计AI 解读

This paper deals with the estimation of linear dynamic models of the autoregressive moving average type for the conditional mean for stationary time series with conditionally heteroskedastic innovation process. Estimation is performed using a particular class of subspace methods that are known to have computational advantages as compared to estimation based on criterion minimization. These advantages are especially strong for high-dimensional time series. Conditions to…

利用子空间方法估计线性动态系统AI 解读

This paper provides a survey on a class of so-called subspace methods whose main proponent is CCA proposed by Larimore (1983, Proceedings of the 1983 American Control Conference 2 ). Because they are based on regressions these methods for the estimation of ARMAX systems are attractive as a result of their conceptual simplicity and their numerical advantages as compared to traditional estimators based on criterion optimization. Under the assumption of correct specification…

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