SOME LIMIT THEORY FOR AUTOCOVARIANCES WHOSE ORDER DEPENDS ON SAMPLE SIZE
研究了当滞后阶数随样本量变化时，变量与其滞后项乘积的样本统计量的弱收敛性质，推导了新的泛函中心极限定理，并应用于单位根检验和异方差协整回归模型。
In this paper we provide some weak convergence results for sample statistics of the product of a variable with its kth-order lag. We assume the variable is a stationary vector that can be represented by linear process, and the lag length k is allowed to be a function of the sample size. Employing the Beveridge–Nelson decomposition, we derive a new functional central limit theorem for this situation and establish related stochastic integral convergence results. We then consider the behavior of associated long-run variance estimators and also extend our analysis to the case where the sample statistics are based on regression residuals. We illustrate the potential range of application of these techniques in the context of (i) testing for I(0) versus I(1) behavior and (ii) estimation and testing in a heteroskedastically cointegrated regression model.We thank the co-editor and the referees for helpful comments on earlier drafts.