A Powerful Test for Linearity When the Order of Integration is Unknown

Abstract

In this paper we propose a test of the null hypothesis of time series linearity against a nonlinear alternative, when uncertainty exists as to whether or not the series contains a unit root. We provide a test statistic that has the same limiting null critical values regardless of whether the series under consideration is generated from a linear I(0) or linear I(1) process, and is consistent against nonlinearity of either form, being asymptotically equivalent to the efficient test in each case. Finite sample simulations show that the new procedure has better size control and offers substantial power gains over the recently proposed robust linearity test of Harvey and Leybourne (2007).

Convergence of Energy Intensity in OECD Countries

“…The series are tested using nonlinearity test developed by Harvey et al, [13]. We selected this test because it has the advantage of not being affected by stationary levels of the variables.…”

“…As suggested in the studies of Harvey et al, [13], maximum number of lags is calculated as (number of lags) 1 4 max int 8 100…”

“…The null hypotheses to use for the test are in the form of In their studies, Harvey et al, [13] suggested the below test statistic that is calculated through aforementioned two tests' statistics when stationary properties of the time series are not exactly known.…”

“…We reviewed whether the series to examine at the first stage of the study for convergence were linear or not by using the test developed by Harvey et al, [13]. are not nonlinear.…”

“…( ) [13]. The main advantage of this test is that results are not affected by the level of stationary.…”