## Bootstrap innovation generation in Stochastic forecast w/ lagged y

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joaomacalos
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Joined: Sat Oct 16, 2021 11:50 pm

### Bootstrap innovation generation in Stochastic forecast w/ lagged y

Good morning,

I'm following the IMFx MOOC in EDX that is implemented in EViews, and I was wondering about how the innovation generation through bootstrapping in stochastic forecasting works. Here is a link for the same lecture on youtube: https://youtu.be/Ca7790HwLwM?list=PLUmH ... sOH2&t=260

The method seems really interesting but I don't feel comfortable using something that I don't understand.

According to the EViews documentation,

"The Innovation generation box on the right side of the dialog determines how the innovations to stochastic equations will be generated. There are two basic methods available for generating the innovations. If Method is set to Normal Random Numbers the innovations will be generated by drawing a set of random numbers from the standard normal distribution. If Method is set to Bootstrap the innovations will be generated by drawing randomly (with replacement) from the set of actual innovations observed within a specified sample".

With some research, and based on this description, I assume that EViews is doing some form of model-based residual boostrapping, resampling from the residuals of the baseline model to add variability to the forecasts. However, I would like to understand better some points:

- The innovations are just being sampled randomly from the residuals and added to the forecasts?

- Is EViews generating new "dependent variable" series using the residuals and then using these new series to generate bootstrapped forecasts?

- If a new dependent variable is generated at each bootstrap run, are the resampled residuals being added to a fitted baseline model, or are they being added to the original time series?

- How does the model simulator deals with the fact that we use a lagged dependent variable as a regressor? Does it account for the potential serial correlation and hence time dependency in the residuals?

- How coefficient uncertainty is passed to the bootstrap estimations?

Thanks!