Bootstrapping Autoregressive Plus Noise Processes

Abstract

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.