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POWER MAXIMIZATION AND SIZE CONTROL IN HETEROSKEDASTICITY AND AUTOCORRELATION ROBUST TESTS WITH EXPONENTIATED KERNELS

Published online by Cambridge University Press:  17 May 2011

Yixiao Sun ,
Peter C.B. Phillips  and
Sainan Jin
Yixiao Sun*
Affiliation:
University of California, San Diego
Peter C.B. Phillips
Affiliation:
Yale University, University of Auckland, University of Southampton, Singapore Management University
Sainan Jin
Affiliation:
Singapore Management University
*
*Address correspondence to Yixiao Sun, Department of Economics, University of California, San Diego, 9500 Gilman Dr., La Jolla, CA 92093-0508; e-mail: yisun@ucsd.edu.
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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 bT HAC testing.

Type
ARTICLES
Information
Econometric Theory , Volume 27 , Issue 6 , December 2011 , pp. 1320 - 1368
Copyright
Copyright © Cambridge University Press 2011

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