Simula@BI: Nonlinear Vector AutoRegressive models and Unit Roots
Simula@BI invites Associate Professor Rickard Sandberg to a seminar about econometrics.
This work derives asymptotic distributions for linearity tests in Vector Smooth Transition AutoRegressive (VSTAR) type of models in the presence of unit roots. The asymptotic distributions of the tests are non-standard because of a unit root assumption. In an extensive set of simulation studies, it is demonstrated that a linearity hypothesis in the presence of unit roots is rejected far too often using standard critical values from a Chi-square distribution. In fact, a linearity hypothesis in a bivariate system can be rejected as often as 60% of the times at a 5% nominal significance level.
Noteworthy is also that the size-problems of the linearity tests magnify with the dimension of the VSTAR model. Quite naturally, these findings will have strong practical implications because VSTAR models often are applied to data that are highly persistent - e.g., to macroeconomic and financial time series data - and the outcomes of standard linearity testing procedures in these cases should be interpreted with caution. To remedy the problem of linearity tests that are grossly over-sized in the presence of unit roots, correct (asymptotic) critical are also provided.
Furthermore, in application to US output growth and interest rate series the situation of linearity testing is demonstrated, and a bootstrapping procedure to correct for the empirical size-problems is also considered.