Structural Changes and Unit Roots: Distinguishing Models of Nonstationary Time Series

The problem of testing the hypothesis of stochastic nonstationarity (structural changes, unit roots) in univariate time series is studied in the paper. A new method of distinguishing between hypotheses of an unknown point of structural break and a unit root is proposed and its properties in the case of dependent observations are studied. The theorem of convergence to zero of the probability of accepting the false hypothesis with the sample size going to the infinity has been proved. Then the method is further analyzed in computer simulations of samples of dependent observations. Finally, applications of the method to econometric time series are considered.