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ROBUST INFERENCE IN AUTOREGRESSIONS WITH MULTIPLE OUTLIERS

Published online by Cambridge University Press:  01 December 2009

Giuseppe Cavaliere and
Iliyan Georgiev
Giuseppe Cavaliere*
Affiliation:
Università di Bologna
Iliyan Georgiev
Affiliation:
Universidade Nova de Lisboa
*
*Address correspondence to Giuseppe Cavaliere, Department of Statistical Sciences, University of Bologna, Via Belle Arti 41, I-40126 Bologna, Italy; e-mail: giuseppe.cavaliere@unibo.it.
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Abstract

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We consider robust methods for estimation and unit root (UR) testing in autoregressions with infrequent outliers whose number, size, and location can be random and unknown. We show that in this setting standard inference based on ordinary least squares estimation of an augumented Dickey–Fuller (ADF) regression may not be reliable, because (a) clusters of outliers may lead to inconsistent estimation of the autoregressive parameters and (b) large outliers induce a jump component in the asymptotic distribution of UR test statistics. In the benchmark case of known outlier location, we discuss why the augmentation of the ADF regression with appropriate dummy variables not only ensures consistent parameter estimation but also gives rise to UR tests with significant power gains, growing with the number and the size of the outliers. In the case of unknown outlier location, the dummy-based approach is compared with a robust, mixed Gaussian, quasi maximum likelihood (QML) approach, novel in this context. It is proved that, when the ordinary innovations are Gaussian, the QML and the dummy-based approach are asymptotically equivalent, yielding UR tests with the same asymptotic size and power. Moreover, as a by-product of QML the outlier dates can be consistently estimated. When the innovations display tails fatter than Gaussian, the QML approach ensures further power gains over the dummy-based method. Simulations show that the QML ADF-type t-test, in conjunction with standard Dickey–Fuller critical values, yields the best combination of finite-sample size and power.

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Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 6: Newbold Conference Special Issue , December 2009, pp. 1625 - 1661
Copyright
Copyright © Cambridge University Press 2009

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