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This paper considers highly persistent time series that are subject tononlinearities in the form of censoring or an occasionally binding constraint,such as are regularly encountered in macroeconomics. A tractable candidatemodel for such series is the dynamic Tobit with a root local to unity. We showthat this model generates a process that converges weakly to a non-standardlimiting process, that is constrained (regulated) to be positive, and derivethe limiting distributions of the OLS estimators of the model parameters. Thisallows inferences to be drawn on the overall persistence of the process (asmeasured by the sum of the autoregressive coefficients), and for the null of aunit root to be tested in the presence of censoring. Our simulations illustratethat the conventional ADF test substantially over-rejects when the data isgenerated by a dynamic Tobit with a unit root. We provide an application of ourmethods 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.

The Local to Unity Dynamic Tobit Model