Adding bootstrapping functionnality from residuals of a model

[Jonathan-87]

Description

It would be interesting to be able to add bootstrapping functionnality from residuals of a model of the time series, this would help :

1. to compute prediction intervals when the method doesn't support it like for regression model (example here : https://otexts.com/fpp3/prediction-intervals.html) and access the full predictive distribution for these models;
2. when a normal distribution for the residuals is an unreasonable assumption boostrapping is a good alternative (example here : https://otexts.com/fpp3/prediction-intervals.html);
3. when we need to compute aggregate of forecast being compute at lower level (example here : https://otexts.com/fpp3/aggregates.html);
4. generate new time series that are similar to our observed series using blocked bootstrap, this can be used for example to compute bagged forecast in order to improve forecast accuracy (https://otexts.com/fpp3/bootstrap.html);

Note that it would be useful also for the mlforecast and neuralforecast library.

Use case

No response

[dsvanidze]

Any updates here? It would be a very useful feature.