Continuous Weak Convergence and Stochastic Equicontinuity Results for Integrated Processes with an Application to the Estimation of a Regression Model
讨论了一阶单整过程的连续和一致弱收敛以及随机等度连续性概念，这些结果可用于推导非线性参数单整和协整系统中估计量和检验统计量的渐近分布，并通过一个带ARMA误差的回归模型展示了其应用。
The concepts of continuous and uniform weak convergence and versions of stochastic equicontinuity are discussed in the context of integrated processes of order one. The considered processes depend on a parameter vector in a specific fashion which is relevant for integrated and cointegrated systems with non-linearities in parameters. The results of the paper can be applied to obtain asymptotic distributions of estimators and test statistics in such systems. In a correctly specified cointegrated Gaussian system, this can be done in a very convenient way. Combining the results of this paper with available general maximum likelihood estimation theories readily shows that the maximum likelihood estimator is asymptotically optimal with a mixed normal limiting distribution. The usefulness of this approach is demonstrated by analyzing a regression model with autoregressive moving average errors and strictly exogenous regressors which may be either integrated of order one, asymptotically stationary, or nonstochastic and bounded.