Applies the sequence of simplifying assumptions of Salcher, Stöckl & Hanke (2026, Section 3.3) to a covariance matrix. Imposing them one after another turns the risk-adjusted forecast error into the ordinary root mean squared error, which is how the paper frames RMSE as a severely restricted special case of RAFE.
Usage
restrict_cov(Sigma, variant = c("none", "cc05", "cc0", "cv", "i"))Details
"none"The covariance is left alone: the full RAFE.
"cc05"All pairwise correlations replaced by \(\rho = 0.5\), variances kept — Equation (17).
"cc0"All correlations set to zero, variances kept; the covariance becomes diagonal.
"cv"Correlations zero and all variances set to the average variance of
Sigma."i"Correlations zero and all variances set to one, giving the identity. With this restriction the mean error is the RMSE of the paper, \(\lVert\hat\mu - \mu\rVert_2\).
References
Salcher, L., Stöckl, S., & Hanke, M. (2026). Lost in Translation? Risk-Adjusting RMSE for Economic Forecast Performance. Journal of Forecasting. doi:10.1002/for.70134
Examples
set.seed(1)
Sigma <- stats::cov(matrix(rnorm(200), 40, 5))
round(stats::cov2cor(restrict_cov(Sigma, "cc05")), 3) # all rho = 0.5
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1.0 0.5 0.5 0.5 0.5
#> [2,] 0.5 1.0 0.5 0.5 0.5
#> [3,] 0.5 0.5 1.0 0.5 0.5
#> [4,] 0.5 0.5 0.5 1.0 0.5
#> [5,] 0.5 0.5 0.5 0.5 1.0
restrict_cov(Sigma, "i") # identity
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1 0 0 0 0
#> [2,] 0 1 0 0 0
#> [3,] 0 0 1 0 0
#> [4,] 0 0 0 1 0
#> [5,] 0 0 0 0 1