Monte Carlo Test for Stochastic Trend in Space State Models for the Location-Scale Family

In space state models for time series, a key point is the decision between modeling the trend of non-stationary processes through a deterministic or a stochastic term. The present paper introduces a Monte Carlo hypothesis test procedure to guide in such a decision. The method works for any time series distribution belonging to the location-scale family. The proposed method provides an alpha-level test for any time series of length greater than 3 and it does not demand assumptions on the distribution of the trend term when it is actually stochastic.