The framework of stationarity testing is extended to allow a generic smooth trend function estimated nonparametrically. The asymptotic behavior of the pseudo-Lagrange multiplier test is analyzed in this setting. The proposed implementation delivers a consistent test whose limiting null...

Let denote the set of absolutely continuous distributions on [0, [infinity]) with finite (infinite) mean. We show the non-existence of a test of H0: versus in the class of sequential tests based on independent identically distributed observations X1,X2,... distributed as F, and which make the...