BLOCK BOOTSTRAP HAC ROBUST TESTS: THE SOPHISTICATION OF THE NAIVE BOOTSTRAP
研究朴素块自助法在长期方差估计中的性质，发现其比标准正态近似更精确，尤其在大带宽时改进显著，为有限样本表现提供理论解释。
This paper studies the properties of naive block bootstrap tests that are scaled by zero frequency spectral density estimators (long-run variance estimators). The naive bootstrap is a bootstrap where the formula used in the bootstrap world to compute standard errors is the same as the formula used on the original data. Simulation evidence shows that the naive bootstrap can be much more accurate than the standard normal approximation. The larger the HAC bandwidth, the greater the improvement. This improvement holds for a large number of popular kernels, including the Bartlett kernel, and it holds when the independent and identically distributed (i.i.d.) bootstrap is used and yet the data are serially correlated. Using recently developed fixed- b asymptotics for HAC robust tests, we provide theoretical results that can explain the finite sample patterns. We show that the block bootstrap, including the special case of the i.i.d. bootstrap, has the same limiting distribution as the fixed- b asymptotic distribution. For the special case of a location model, we provide theoretical results that suggest the naive bootstrap can be more accurate than the standard normal approximation depending on the choice of the bandwidth and the number of finite moments in the data. Our theoretical results lay the foundation for a bootstrap asymptotic theory that is an alternative to the traditional approach based on Edgeworth expansions.