A NEW ASYMPTOTIC THEORY FOR HETEROSKEDASTICITY-AUTOCORRELATION ROBUST TESTS
提出一种新的渐近理论，将带宽设为样本量的固定比例，更准确地刻画异方差自相关稳健检验中带宽和核函数的影响，并通过模拟验证其优于传统渐近方法。
A new first-order asymptotic theory for heteroskedasticity-autocorrelation (HAC) robust tests based on nonparametric covariance matrix estimators is developed. The bandwidth of the covariance matrix estimator is modeled as a fixed proportion of the sample size. This leads to a distribution theory for HAC robust tests that explicitly captures the choice of bandwidth and kernel. This contrasts with the traditional asymptotics (where the bandwidth increases more slowly than the sample size) where the asymptotic distributions of HAC robust tests do not depend on the bandwidth or kernel. Finite-sample simulations show that the new approach is more accurate than the traditional asymptotics. The impact of bandwidth and kernel choice on size and power of t-tests is analyzed. Smaller bandwidths lead to tests with higher power but greater size distortions, and large bandwidths lead to tests with lower power but smaller size distortions. Size distortions across bandwidths increase as the serial correlation in the data becomes stronger. Overall, the results clearly indicate that for bandwidth and kernel choice there is a trade-off between size distortions and power. Finite-sample performance using the new asymptotics is comparable to the bootstrap, which suggests that the asymptotic theory in this paper could be useful in understanding the theoretical properties of the bootstrap when applied to HAC robust tests.We thank an editor and a referee for constructive comments on a previous version of the paper. Helpful comments provided by Cliff Hurvich, Andy Levin, Jeff Simonoff, and seminar participants at NYU (Statistics), U. Texas Austin, Yale, U. Montreal, UCSD, UC Riverside, UC Berkeley, U. of Pittsburgh, SUNY Albany, U. Aarhus, Brown U., NBER/NSF Time Series Conference, and 2003 Winter Meetings of the Econometrics Society are gratefully acknowledged. We gratefully acknowledge financial support from the National Science Foundation through grant SES-0095211. We thank the Center for Analytic Economics at Cornell University.