Abstract :
We consider two tests of structural change for partially linear time-series models.
The first tests for structural change in the parametric component, based on the
cumulative sums of gradients from a single semiparametric regression. The second
tests for structural change in the parametric and nonparametric components simultaneously,
based on the cumulative sums of weighted residuals from the same semiparametric
regression. We derive the limiting distributions of both tests under the
null hypothesis of no structural change and for sequences of local alternatives. We
show that the tests are generally not asymptotically pivotal under the null but may
be free of nuisance parameters asymptotically under further asymptotic stationarity
conditions. Our tests thus complement the conventional instability tests for parametric
models. To improve the finite-sample performance of our tests, we also propose
a wild bootstrap version of our tests and justify its validity. Finally, we conduct a
small set of Monte Carlo simulations to investigate the finite-sample properties of
the tests.
