Discussion Paper 1007, "Threshold Autoregressions Under Near Integratedness", by Pitarakis, J.
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 under persistent regressors where it is well known that the noncentrality parameter appears in the limiting distribution of test statistics, making them impractical for inference purposes.
Keynames: Threshold Autoregressive Models, Near Unit Root, Noncentrality Parameter, Nonlinear time series
JEL Classification: C22.