Bootstrapping Autoregressive Plus Noise Processes

We address the problem of estimating confidence intervals for the parameters of an autoregressive plus noise process, in particular when the additive noise is non-Gaussian. We demonstrate how the independent data bootstrap can be used to solve this problem. We motivate an autoregressive moving-average modeling approach and apply the recursive maximum algorithm for parameter estimation. Computer simulations are carried out to show the performance of the proposed method. Furthermore a real data example from automotive engineering has been considered for assessing our approach. Using a pressure signal from inside the combustion chamber, we show how confidence intervals for the autoregressive parameters can be calculated.