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Bimodal t-ratios: the impact of thick tails on inference

Bimodal t-ratios: the impact of thick tails on inference
Bimodal t-ratios: the impact of thick tails on inference
This paper studies the distribution of the classical t-ratio with data generated from distributions with no finite moments and shows how classical testing is affected by bimodality. A key condition in generating bimodality is independence of the observations in the underlying data-generating process (DGP). The paper highlights the strikingly different implications of lack of correlation versus statistical independence in DGPs with infinite moments and shows how standard inference can be invalidated in such cases, thereby pointing to the need for adapting estimation and inference procedures to the special problems induced by thick-tailed (TT) distributions. The paper presents theoretical results for the Cauchy case and develops a new distribution termed the 'double-Pareto', which allows the thickness of the tails and the existence of moments to be determined parametrically. It also investigates the relative importance of tail thickness in case of finite moments by using TT distributions truncated on a compact support, showing that bimodality can persist even in such cases. Simulation results highlight the dangers of relying on naive testing in the face of TT distributions. Novel density estimation kernel methods are employed, given that our theoretical results yield cases that exhibit density discontinuities.
bimodality, cauchy, double-pareto, thick tails, t-ratio
1368-4221
271-289
Fiorio, Carlo V.
f2b4f4bd-1cd6-4b4f-aa45-b1cc43be464a
Hajivassiliou, Vassilis
bbe50d72-9848-40ca-98b3-01b2455e0057
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243
Fiorio, Carlo V.
f2b4f4bd-1cd6-4b4f-aa45-b1cc43be464a
Hajivassiliou, Vassilis
bbe50d72-9848-40ca-98b3-01b2455e0057
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243

Fiorio, Carlo V., Hajivassiliou, Vassilis and Phillips, Peter C.B. (2010) Bimodal t-ratios: the impact of thick tails on inference. The Econometrics Journal, 13 (2), 271-289. (doi:10.1111/j.1368-423X.2010.00315.x).

Record type: Article

Abstract

This paper studies the distribution of the classical t-ratio with data generated from distributions with no finite moments and shows how classical testing is affected by bimodality. A key condition in generating bimodality is independence of the observations in the underlying data-generating process (DGP). The paper highlights the strikingly different implications of lack of correlation versus statistical independence in DGPs with infinite moments and shows how standard inference can be invalidated in such cases, thereby pointing to the need for adapting estimation and inference procedures to the special problems induced by thick-tailed (TT) distributions. The paper presents theoretical results for the Cauchy case and develops a new distribution termed the 'double-Pareto', which allows the thickness of the tails and the existence of moments to be determined parametrically. It also investigates the relative importance of tail thickness in case of finite moments by using TT distributions truncated on a compact support, showing that bimodality can persist even in such cases. Simulation results highlight the dangers of relying on naive testing in the face of TT distributions. Novel density estimation kernel methods are employed, given that our theoretical results yield cases that exhibit density discontinuities.

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More information

Published date: 7 May 2010
Keywords: bimodality, cauchy, double-pareto, thick tails, t-ratio

Identifiers

Local EPrints ID: 157285
URI: http://eprints.soton.ac.uk/id/eprint/157285
ISSN: 1368-4221
PURE UUID: 7f928759-b12d-4f4c-a004-5966bd00bc1c
ORCID for Peter C.B. Phillips: ORCID iD orcid.org/0000-0003-2341-0451

Catalogue record

Date deposited: 04 Jun 2010 10:16
Last modified: 14 Mar 2024 01:46

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Contributors

Author: Carlo V. Fiorio
Author: Vassilis Hajivassiliou

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