Moment condition tests for heavy tailed time series

Jonathan B. Hill and Mike Aguilar

Journal of Econometrics, 2013, vol. 172, issue 2, 255-274

Abstract: We develop an asymptotically chi-squared statistic for testing moment conditions E[mt(θ0)]=0, where mt(θ0) may be weakly dependent, scalar components of mt(θ0) may have an infinite variance, and E[mt(θ)] need not exist for any θ under the alternative. Score tests are a natural application, and in general a variety of tests can be heavy-tail robustified by our method, including white noise, GARCH affects, omitted variables, distribution, functional form, causation, volatility spillover and over-identification. The test statistic is derived from a tail-trimmed sample version of the moments evaluated at a consistent plug-in θˆT for θ0. Depending on the test in question and heaviness of tails, θˆT may be any consistent estimator including sub-T1/2-convergent and/or asymptotically non-Gaussian ones, since θˆT can be assured not to affect the test statistic asymptotically. We adapt bootstrap, p-value occupation time, and covariance determinant methods for selecting the trimming fractile in any sample, and apply our statistic to tests of white noise, omitted variables and volatility spillover. We find it obtains sharp empirical size and strong power, while conventional tests exhibit size distortions.

Keywords: Moment condition test; Heavy tails; Tail trimming; Robust inference (search for similar items in EconPapers)
JEL-codes: C13 C20 C22 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:172:y:2013:i:2:p:255-274

DOI: 10.1016/j.jeconom.2012.08.013

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