Estimation and Testing of Cointegrated Systems by an Autoregressive Approximation
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通过自回归近似估计与检验协整系统
- 研究问题
- 在不假定数据生成过程具有有限阶参数表示时，如何估计一般协整系统，并检验预先设定的协整秩与归一化限制？
- 方法与思路
- 作者使用随样本量适当增长的自回归阶数，构造协整向量及误差修正权重矩阵的最小二乘估计，并推导估计与检验的极限理论。
- 材料陈述的贡献
- 摘要称，方法放宽有限阶自回归限制，提供常规渐近卡方 Wald 检验和非标准设定检验，并给出零频谱解释。
- 阅读关注点
- 应核对自回归阶数增长条件、协整秩及归一化的处理，区分常规 Wald 与设定检验的分布，并理解零频谱对应关系。
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- 仅据所给 Crossref 摘要，阶数选择、临界值计算和有限样本表现未说明；最大似然关系仅在所述特殊情形讨论。
原文摘要
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 assumptions are also provided. The asymptotic distributions of the estimators and test statistics are derived by assuming that the order of the auto-regressive approximation increases with the sample size at a suitable rate. This generalizes some previous results derived for finite-order autoregressions as no assumption of a finite-parameter data-generating process is imposed. The estimators and tests of the paper are interpreted in terms of autoregressive spectral density estimators at the zero frequency and, in the special case of a finite-order Gaussian autoregression, their relation to maximum likelihood procedures is discussed. All estimators of the paper can be applied with simple least-squares techniques and used to construct conventional Wald tests with asymptotic chi-square distributions under the null hypothesis. The limit theory of the specification tests is nonstandard, similar to that in univariate unit root tests.