Detecting exponential component in autoregressive models: comparative study between several tests of nonlinearity

In this work, we focus on tests able to detect the eventual existence of an exponential component in autoregressive models of order 1. We propose a comparative study by simulation between several tests selected for this purpose. Thus, we put on competition the tests of Hinich (1982), Keenan (1985), Tsay (1986), Saikkonen and Luukkonen (1988) with the pseudo-Gaussian test developed by Allal and El Melhaoui (2006). The investigation of these tests, allowed us to discover that the pseudo-Gaussian test depends on a nuisance appearing only under the alternative. We suggest a transformation of the pseudo-Gaussian test statistic to overcome this problem. The simulation results show that the pseudo-Gaussian test based on this transformation has the best performance in detecting the exponential component, which encourages us to run a simulation study to investigate the ability of this test to detect other types of nonlinearity.