Bootstrapping TSMARS models

We investigate bootstrap inference methods for nonlinear time series models obtained using Multivariate Adaptive Regression Splines for Time Series (TSMARS), for which theoretical properties are not currently known. We use two different methods of bootstrapping to obtain confidence intervals for the underlying nonlinear function and prediction intervals for future values, based on estimated TSMARS models for the bootstrapped data. We also explore the method of Bootstrap AGGregatING (Bagging), due to Breiman (1996), to investigate whether the residual and prediction mean squared errors from a fitted TSMARS model can be reduced by averaging across the values obtained from each of the bootstrapped models. We find that, although the estimated parameters of models obtained using TSMARS may differ markedly from one bootstrap replicate to another, fitted values from the estimated models are relatively stable. We also find that Bagging can lead to smaller residual and forecasts errors, but that confidence and prediction intervals based on bootstrapping have a coverage that is much too small