"Asymptotic behaviour of the CUSUM of squares test under stochastic and
deterministic time trends"

Bent Nielsen & Jouni Sohkanen
Department of Economics, University of Oxford

Econometric Theory 27, 913-927 (2011).

Abstract:
We generalize the cumulative sum of squares (CUSQ) test to the case of
non-stationary autoregressive distributed lag models with deterministic
time trends. The test may be implemented with either ordinary least squares
residuals or standardized forecast errors. In explosive cases the asymptotic
theory applies more generally for the least squares residuals based test.
Preliminary simulations of the tests suggest a very modest difference
between the tests and a very modest variation with nuisance parameters.
This supports the use of the tests in explorative analysis.