Nonlinear dynamics in economics and finance and unit root testing

The recent financial crisis exposed the inability of traditional theoretical and empirical models to parsimoniously capture the rich dynamics of the economic environment. This has stimulated the interest of both academics and practitioners in the development and application of more sophisticated models. By allowing for the presence of nonlinearities, complex dynamics, multiple equilibria, structural breaks and spurious trends, these latter models resemble more closely the properties of economic and financial time series. In this article, we illustrate the flexibility of a family of econometric models, namely the exponential smooth transition autoregressive (ESTAR), to encompass several of the above characteristics. We then re-assess the power of the ESTAR unit root test developed by Kapetanios, Shin and Snell ((2003) Kapetanios, G., Shin, Y. and Snell, A. 2003. Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics, 112(2): 359–79. (doi:10.1016/S0304-4076(02)00202-6)Crossref], Web of Science ®] , Google Scholar]) in the presence of nuisance parameters typically encountered in the literature and compare its performance with that of the augmented Dickey-Fuller and the Enders and Granger ((1998) Enders, W. and Granger, C. W.J. 1998. Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics, 16(3): 304–11. Taylor & Francis Online], Web of Science ®] , Google Scholar]) tests. Our results show the lack of dominance of any particular test and that the power is not independent to priors about the nuisance parameters. Finally, we examine several asset price deviations from fundamentals and one hyper-inflation series and find contradictory results between the nonlinear fitted models and unit root tests. The findings highlight that new testing procedures with higher power are desirable in order to shed light on the behavior of financial and economic series.