Threshold Autoregressions Under Near Integratedness

7 Pages Posted: 5 Mar 2011

See all articles by Jean-Yves Pitarakis

Jean-Yves Pitarakis

University of Southampton - Division of Economics

Date Written: November 1, 2010


We explore the properties of a Wald type test statistic for detecting the presence of threshold effects in time series when the underlying process could be nearly integrated as opposed to having an exact unit root. We derive its limiting distribution and establish its equivalence to a normalised squared Brownian Bridge process. More importantly we show that the limiting random variable no longer depends on the noncentrality parameter characterising the nearly integrated DGP. This is an unusual occurrence which is in stark contrast with the existing literature on conducting inferences with persistent processes under linearity where it is well known that the noncentrality parameter appears in the limiting distribution of test statistics, making them impractical for inference purposes.

Keywords: Threshold Autoregressive Models, Near Unit Root, Noncentrality Parameter, Nonlinear

JEL Classification: C22, C50

Suggested Citation

Pitarakis, Jean-Yves, Threshold Autoregressions Under Near Integratedness (November 1, 2010). Available at SSRN: or

Jean-Yves Pitarakis (Contact Author)

University of Southampton - Division of Economics ( email )

Southampton, SO17 1BJ
United Kingdom
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