forecast.VAR takes sqrt of potentially negative covariance

[FinYang]

Currently, forecast.VAR calculates sqrt of the covariance matrix:

fable/R/var.R

Line 244 in 9b926f8

sigma <- map(sigma, sqrt)

and then recovers the covariance matrix before constructing the distribution at the end:

fable/R/var.R

Line 266 in 9b926f8

unname(distributional::dist_multivariate_normal(split(fc, row(fc)), map(sigma, `^`, 2)))

This produces NaN when the covariance between variables is negative. For example:

library(tidyverse)
library(fable)
#> Loading required package: fabletools
lung_deaths <- cbind(mdeaths, fdeaths) %>%
  as_tsibble(pivot_longer = FALSE)

fit <- lung_deaths %>%
  mutate(fdeaths = -fdeaths) %>% 
  model(VAR(vars(mdeaths, fdeaths) ~ AR(3)))

fc <- forecast(fit, h=1)
#> Warning: There was 1 warning in `mutate()`.
#> ℹ In argument: `VAR(vars(mdeaths, fdeaths) ~ AR(3)) = (function (object, ...)
#>   ...`.
#> Caused by warning in `FUN()`:
#> ! NaNs produced
distributional::covariance(pull(fc, .distribution))
#> [[1]]
#>          mdeaths fdeaths
#> mdeaths 58985.95     NaN
#> fdeaths      NaN 9983.95

^{Created on 2023-04-12 with reprex v2.0.2}