Solving stochastically the VAR model assuming a normal error distribution

[nickcox896]

In some software, like Eviews, we can solve stochastically the VAR model.
Solving a VAR model stochastically in EViews means running a forecasting simulation that
incorporates the model's random error terms (residuals) rather than setting them to zero (deterministic).
This technique simulates potential future shocks to generate confidence intervals for forecasts,
providing a range of likely outcomes rather than a single point estimate.
We can select to use Random Normal Residuals, or Bootstrap methods to simulate the errors.

If I want to simulate from a normal distribution how can I do that with the fable package? For example:

library(fpp3)
h <- 10
times <- 1000
fc<- us_change |>  model(VAR(vars(Consumption, Income) ~ AR(2))) 

For point forecasts we can use:

fc %>% forecast(h = h)

To solve stochastically the VAR assuming no particular error distribution we use bootstrapping

fc %>% forecast(h = h, bootstrap = TRUE, times=times)

If we want to solve stochastically the VAR assuming normal error distribution how can we do that?

[robjhyndman]

The forecasts produced from fable are already probabilistic, taking account of the variation in future shocks. That's why we provide the forecast as a distribution. The point forecast is the mean of the distribution, which we also provide. By default, the errors are assumed normal, but setting bootstrap = TRUE allows for non-normality by resampling residuals.

[nickcox896]

thank you !