Bootstrap Tests of Stationarity

James Morley, Washington University in St. Louis
Tara M. Sinclair, George Washington University

Abstract

We compare the finite-sample performance of different stationarity tests. Monte Carlo analysis reveals that tests based on Lagrange multiplier (LM) statistics with nonstandard asymptotic distributions reject far more often than their nominal size for trend-stationary processes of the kind estimated for macroeconomic data. Bootstrap versions of these LM tests have empirical rejection probabilities that are closer to nominal size, but they still tend to over-reject. Meanwhile, we find that a bootstrap likelihood ratio (LR) est has very accurate finite-sample size, while at the same time having higher power than the bootstrap LM tests against empirically relevant nonstationary alternatives. Based on the bootstrap LR test, and in some cases contrary to the bootstrap LM tests, we can reject trend stationarity for US real GDP, the unemployment rate, consumer prices, and payroll employment in favour of unit root processes with large permanent movements.