An ARIMA(p,l,0) signal disturbed by MA(q) noise is an ARIMA(p,l, p+q+1) process restricted by nonlinear constraints on parameters. For this model with a unit root the restricted maximum likelihood estimator (RMLE) of the unit root is strongly consistent and it has the same limiting distribution as the ordinary least squares estimator of the unit root in an AR(1) model tabulated by Dickey and Fuller (1979). A modified RMLE is proposed which has the same limiting properties as the RMLE and is computationally much simpler. Simulation results show that our unit root tests based on the modified RMLE perform very well for small samples and compare favorably with the Said and Dickey (1985) tests with respect to both sizes and powers. An illustrative example from sample survey is given.
- large sample
- maximum likelihood estimation
- measurement error
- Monte Carlo study
- restricted ARIMA model