Comparing the robustness of tests for stochastic versus deterministic trend in time series

In time series analysis, the decision of modeling the trend term as a stochastic or a deterministic component is a primordial step. For decades, authors have been focused on developing statistical tests to guide the analysts in such a decision. Surprisingly, less attention has been given to evaluate the robustness of the methods. This paper compares the robustness of four of the prominent tests. For this, various scenarios were used considering (i) the actual distribution of the noise term, (ii) the sample size, and (iii) the actual time series structure among auto-regressive moving average, linear structural space state, and the exponential generalize auto-regressive conditional heteroskedasticity models. An example of application on the Brazilian Gross Domestic Product is used to discuss the behavior of the methods vis-& agrave;-vis to their inferred robustness.