This paper considers highly persistent time series that are subject to nonlinearities in the form of censoring or an occasionally binding constraint, such as are regularly
encountered in macroeconomics. A tractable candidate model for such series is the dynamic
Tobit with a root local to unity. We show that this model generates a process that converges
weakly to a non-standard limiting process, that is constrained (regulated) to be positive.
Surprisingly, despite the presence of censoring, the OLS estimators of the model parameters
are consistent. We show that this allows OLS-based inferences to be drawn on the overall
persistence of the process (as measured by the sum of the autoregressive coefficients), and for
the null of a unit root to be tested in the presence of censoring. Our simulations illustrate
that the conventional ADF test substantially over-rejects when the data is generated by a
dynamic Tobit with a unit root, whereas our proposed test is correctly sized. We provide an
application of our methods to testing for a unit root in the Swiss franc / euro exchange rate,
during a period when this was subject to an occasionally binding lower bound.
unit root test
,dynamic Tobit
,local unit root
,non-negative time series
