Power Maximization and Size Control in Heteroskedasticity and Autocorrelation Robust Tests with Exponentiated Kernels

Yixiao Sun, Peter Phillips and Sainan Jin

No 1749, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 (rho). We show that the nonstandard fixed-rho limit distributions of the t-statistic provide more accurate approximations to the finite sample distributions than the conventional large-rho 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-rho 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; KV), and yet it does not incur the power loss that often hurts the performance of the latter test. The new test therefore combines the advantages of the KV test and the standard (MSE optimal) HAC test while avoiding their main disadvantages (power loss and size distortion, respectively). The results complement recent work by Sun, Phillips and Jin (2008) on conventional and bT HAC 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 (search for similar items in EconPapers)
JEL-codes: C13 C14 C22 C51 (search for similar items in EconPapers)
Pages: 50 pages
Date: 2010
New Economics Papers: this item is included in nep-ets and nep-sea
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Published in Econometric Theory (December 2011), 27(6): 1320-1368

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Journal Article: POWER MAXIMIZATION AND SIZE CONTROL IN HETEROSKEDASTICITY AND AUTOCORRELATION ROBUST TESTS WITH EXPONENTIATED KERNELS (2011)
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