 Solution

The interval treats the selected model and estimated detrending and seasonal components as fixed, often assumes approximately Gaussian homoscedastic innovations, and ignores model-selection and parameter uncertainty. With only 100 observations these omissions can materially reduce coverage. A residual or parametric bootstrap that repeats decomposition, model selection, fitting, and forecasting can propagate those sources of uncertainty; time-series cross-validation can additionally assess empirical one-step coverage.