Publication Type

Journal Article

Version

publishedVersion

Publication Date

12-2011

Abstract

Using the power kernels of Phillips, Sun, and Jin (2006, 2007), we examine the large sample asymptotic properties of the t-test for different choices of power parameter (ρ). We show that the nonstandard fixed-ρ limit distributions of the t-statistic provide more accurate approximations to the finite sample distributions than the conventional large-ρ limit distribution. We prove that the second-order corrected critical value based on an asymptotic expansion of the nonstandard limit distribution is also second-order correct under the large-ρ asymptotics. As a further contribution, we propose a new practical procedure for selecting the test-optimal power parameter that addresses the central concern of hypothesis testing: The selected power parameter is test-optimal in the sense that it minimizes the type II error while controlling for the type I error. A plug-in procedure for implementing the test-optimal power parameter is suggested. Simulations indicate that the new test is as accurate in size as the nonstandard test of Kiefer and Vogelsang (2002a, 2002b), and yet it does not incur the power loss that often hurts the performance of the latter test. The results complement recent work by Sun, Phillips, and Jin (2008) on conventional and bTHAC testing.

Keywords

Asymptotic expansion, HAC estimation, Long run variance, Loss function, Optimal smoothing parameter, Power kernel, Power maximization, Size control, Type I error, Type II error

Discipline

Econometrics | Economic Theory

Research Areas

Econometrics

Publication

Econometric Theory

Volume

27

Issue

6

First Page

1320

Last Page

1368

ISSN

0266-4666

Identifier

10.1017/S0266466611000077

Publisher

Cambridge University Press

Additional URL

https://doi.org/10.1017/S0266466611000077

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