A Gaussian test for unit roots with an application to great ratios

Tilak Abeysinghe, Gulasekaran Rajaguru

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Abstract

Non-standard distributions are a common feature of many tests for unit-roots and cointegration that are currently available. The main problem with non-standard distributions is that when the true data generating process is unknown, which is the case in general, it is not easy to engage in a specification search because the distribution changes as the specification changes, especially with respect to deterministic components. We use a mixed-frequency regression technique to develop a test for cointegration under the null of stationarity of the deviations from a long-run relationship. What is noteworthy about this MA unit root test, based on a variance-difference, is that, instead of having to deal with non-standard distributions, it takes testing back to the normal distribution and offers a way to increase power without having to increase the sample size substantially. Monte Carlo simulations show minimal size distortions even when the AR root is close to unity and that the test offers substantial gains in power against near-null alternatives in moderate size samples. Although the null of stationarity is the research line to be pursued, we also consider an extension of the procedure to cover the AR unit root case that provides a Gaussian test with more power. An empirical exercise illustrates the relative usefulness of the test further.
Original languageEnglish
Title of host publication52nd Annual Conference of the NZ Association of Economists Proceedings
EditorsB Kaye-Blake
Place of PublicationNew Zealand
PublisherNew Zealand Association of Economists
Number of pages38
Publication statusPublished - 2011
EventAnnual Conference of the New Zealand Association of Economics - Amora Hotel, Wellington, New Zealand
Duration: 29 Jun 20111 Jul 2011
Conference number: 52
http://www.nzae.org.nz/event/nzae-conference-2011/

Conference

ConferenceAnnual Conference of the New Zealand Association of Economics
Abbreviated titleNZAE
CountryNew Zealand
CityWellington
Period29/06/111/07/11
Internet address

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Unit root
Sample size
Stationarity
Cointegration
Size distortion
Usefulness
Long-run relationship
Common features
Backtesting
Unit root tests
Exercise
Data generating process
Normal distribution
Monte Carlo simulation
Deviation

Cite this

Abeysinghe, T., & Rajaguru, G. (2011). A Gaussian test for unit roots with an application to great ratios. In B. Kaye-Blake (Ed.), 52nd Annual Conference of the NZ Association of Economists Proceedings New Zealand: New Zealand Association of Economists .
Abeysinghe, Tilak ; Rajaguru, Gulasekaran. / A Gaussian test for unit roots with an application to great ratios. 52nd Annual Conference of the NZ Association of Economists Proceedings. editor / B Kaye-Blake. New Zealand : New Zealand Association of Economists , 2011.
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Abeysinghe, T & Rajaguru, G 2011, A Gaussian test for unit roots with an application to great ratios. in B Kaye-Blake (ed.), 52nd Annual Conference of the NZ Association of Economists Proceedings. New Zealand Association of Economists , New Zealand, Annual Conference of the New Zealand Association of Economics, Wellington, New Zealand, 29/06/11.

A Gaussian test for unit roots with an application to great ratios. / Abeysinghe, Tilak; Rajaguru, Gulasekaran.

52nd Annual Conference of the NZ Association of Economists Proceedings. ed. / B Kaye-Blake. New Zealand : New Zealand Association of Economists , 2011.

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

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AB - Non-standard distributions are a common feature of many tests for unit-roots and cointegration that are currently available. The main problem with non-standard distributions is that when the true data generating process is unknown, which is the case in general, it is not easy to engage in a specification search because the distribution changes as the specification changes, especially with respect to deterministic components. We use a mixed-frequency regression technique to develop a test for cointegration under the null of stationarity of the deviations from a long-run relationship. What is noteworthy about this MA unit root test, based on a variance-difference, is that, instead of having to deal with non-standard distributions, it takes testing back to the normal distribution and offers a way to increase power without having to increase the sample size substantially. Monte Carlo simulations show minimal size distortions even when the AR root is close to unity and that the test offers substantial gains in power against near-null alternatives in moderate size samples. Although the null of stationarity is the research line to be pursued, we also consider an extension of the procedure to cover the AR unit root case that provides a Gaussian test with more power. An empirical exercise illustrates the relative usefulness of the test further.

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Abeysinghe T, Rajaguru G. A Gaussian test for unit roots with an application to great ratios. In Kaye-Blake B, editor, 52nd Annual Conference of the NZ Association of Economists Proceedings. New Zealand: New Zealand Association of Economists . 2011