A double bootstrap method to analyze linear models with autoregressive error terms

A new method for the analysis of linear models that have autoregressive errors is proposed. The approach is not only relevant in the behavioral sciences for analyzing small-sample time-series intervention models, but it is also appropriate for a wide class of small-sample linear model problems in which there is interest in inferential statements regarding all regression parameters and autoregressive parameters in the model. The methodology includes a double application of bootstrap procedures. The 1st application is used to obtain bias-adjusted estimates of the autoregressive parameters. The 2nd application is used to estimate the standard errors of the parameter estimates. Theoretical and Monte Carlo results are presented to demonstrate asymptotic and small-sample properties of the method; examples that illustrate advantages of the new approach over established time-series methods are described.