Date of Award
Doctor of Philosophy
Dr. Joeseph McKean
Dr. Bradley Huitema
The analysis of a particular time-series intervention model involving lag one autoregressive (AR(1)) error terms is the focus of this dissertation. The method of ordinary least squares, and several two stage procedures that are commonly used to analyze this intervention model are examined. The two stage Cochrane-Orcutte, Durbin, and generalized least squares procedures each requires estimation of the AR(1) parameter in stage one before hypothesis testing about the intervention parameters can be performed in stage two. Using Monte Carlo experiments we show that the AR(1) estimates commonly used in these procedures are poor and consequently the stage two hypothesis tests are unreliable. Simulation results confirm also that ordinary least squares analysis is inappropriate because the error terms are not independent.
A bootstrap alternative method is developed and the theory presented. Results from Monte Carlo experiments show that the bootstrap method improves estimation of the AR(1) parameter and is more reliable with respect to hypothesis testing about the model parameters. Generalization of the bootstrap method to the intervention model with lag q autoregressive (AR(q)) error terms is developed and demonstrated in simulations of the model with AR(2) errors.
Several rank based estimates of the AR(1) parameter are investigated with respect to their robustness to contamination of the error terms. The robustness of the bootstrap hypothesis testing method to misidentification of the error terms is also investigated.
McKnight, Scott D., "A Bootstrap Method to Analyze an Intervention Model with Autoregressive Error Terms" (1994). Dissertations. 1819.