Let's Fix It: Fixed-b Asymptotics versus Small-b Asymptotics in Heteroskedasticity and Autocorrelation Robust Inference

By Yixiao Sun. 2010

124 citations recorded by the source corpus.

In the presence of heteroscedasticity and autocorrelation of unknown forms, the covariance matrix of the parameter estimator is often estimated using a nonparametric kernel method that involves a lag truncation parameter. Depending on whether this lag truncation parameter is specified to grow at a slower rate than or the same rate as the sample size, we obtain two types of asymptotic approximations: the small-b asymptotics and the fixed-b asymptotics. Using techniques for probability distribution approximation and high order expansions, this paper shows that the fixed-b asymptotic approximation provides a higher order refinement to the first order small-b asymptotics. This result provides a theoretical justification on the use of the fixed-b asymptotics in empirical applications. On the basis of the fixed-b asymptotics and higher order small-b asymptotics, the paper introduces a new and easy-to-use asymptotic F test that employs a finite sample corrected Wald statistic and uses an F-distribution as the reference distribution. Finally, the paper develops a bandwidth selection rule that is testing-optimal in that the bandwidth minimizes the type II error of the asymptotic F test while controlling for its type I error. Monte Carlo simulations show that the asymptotic F test with the testing-optimal bandwidth works very well in finite samples.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7b34e90c9842b1fc9ca249dc6fcdd6295268a2f1

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Citations in the corpus

Should we go one step further? An accurate comparison of one-step and two-step procedures in a generalized method of moments framework (2018, unknown): “Part (b) is a special case of Theorem 6(a) of Sun (2014b) with G = [Id; Od q]0: It remains to prove part (a).”
Robust Trend Inference with Series Variance Estimator and Testing-Optimal Smoothing Parameter (2011, methodology): “The method in Sun (2010) can be adopted for trend estimation and inference, leading to a testing-oriented bandwidth choice for the VF type test.”
BUSINESS CYCLES, TREND ELIMINATION, AND THE HP FILTER (2020, unknown): “…the use of finite series representations in terms of deterministic functions for empirical trend modeling and low frequency projection methods in the work of Hwang and Sun (2018), Phillips (2001b, 2005a, 2005b, 2014), Müller (2007), Müller and Watson, 2018), Sun (2014), Yamada (2020) and others.”