For autoregressive moving averages with time trends and autoregressive unit roots, the consistency of the maximum likelihood estimators is established. General uniform approximations are established for the quadratic forms which appear in the Gaussian likelihood.
Bibliographical noteFunding Information:
The authors wish to thank a referee for valuable comments. This work was supported by grant No. 1999-1-104-001-5 from the interdisciplinary research grant of KOSEF.
- Autoregressive moving average
- Lagrangian multiplier test
- Likelihood ratio test
- Primary 62M10
- Stationary null hypothesis
- Unit root test