Co-summability and NLLS Regressions: Generalizing Co-integration for Nonlinear Models
|Speaker:||Vanessa Berenguer-Rico, University of Oxford|
|Date:||Friday 9 May 2014|
|Time:||16.15 - 17.45|
|Location:||Streatham Court B|
Co-integration plays a fundamental role in the econometric analysis of linear relationships among persistent economic time series. Nonetheless, nonlinearities are often encountered in modern macroeconometric models that account for more flexible relationships. In a nonlinear world, however, the concepts order of integration and co-integration are no long valid. The inherent linearity in the order of integration idea invalidates its use to characterize nonlinear persistent processes and this, in turn, implies that co-integration cannot be directly extended to study nonlinear relationships. To overcome these hindrances, Berenguer-Rico and Gonzalo (2013a) formalized the concept order of summability of a stochastic process which generalizes the order of integration idea to non-linear time series. Subsequently, Berenguer- Rico and Gonzalo (2013b) developed co-summability theory to open co-integration to nonlinear relationships. The statistical analysis was based on regression models that are nonlinear in variables but linear in parameters and hence the OLS estimator was considered when testing for co-summability from a residual based test. In this paper, NLLS regressions are analysed and a test for co-summability is proposed. Specifically, the asymptotic properties of the NLLS estimator under (i) no co-summability, i.e. spurious regressions, and (ii) co-summability, possibly misspecified, are considered. Given these asymptotic properties, a residual based test for co-summability can be designed, which can also be seen as a misspecification testing procedure. The finite sample performance of the test is examined through several Monte Carlo experiments. To show the empirical relevance of the proposed theory and tools, intrinsic bubbles, hyperinflations and aggregate consumption models are examined making use if the co-summability toolkit.
Here is a link to the seminar paper: www.vanessaberenguer.com/research/CosummabilityNLLS/Co-summabilityNLLS.pdf