csprojmat: Projection matrix for optimal combination cross-sectional...

In FoReco: Forecast Reconciliation

Projection matrix for optimal combination cross-sectional reconciliation

Description

This function computes the projection or the mapping matrix \mathbf{M} and \mathbf{G}, respectively, such that \widetilde{\mathbf{y}} = \mathbf{M}\widehat{\mathbf{y}} = \mathbf{S}_{cs}\mathbf{G}\widehat{\mathbf{y}}, where \widetilde{\mathbf{y}} is the vector of the reconciled forecasts, \widehat{\mathbf{y}} is the vector of the base forecasts, \mathbf{S}_{cs} is the cross-sectional structural matrix, and \mathbf{M} = \mathbf{S}_{cs}\mathbf{G}. For further information regarding on the structure of these matrices, refer to Girolimetto et al. (2023).

Usage

csprojmat(agg_mat, cons_mat, comb = "ols", res = NULL, mat = "M", ...)

Arguments

agg_mat	A (n_a \times n_b) numeric matrix representing the cross-sectional aggregation matrix. It maps the n_b bottom-level (free) variables into the n_a upper (constrained) variables.
cons_mat	A (n_a \times n) numeric matrix representing the cross-sectional zero constraints. It spans the null space for the reconciled forecasts.
comb	A string specifying the reconciliation method. For a complete list, see cscov.
res	An (N \times n) optional numeric matrix containing the in-sample residuals. This matrix is used to compute some covariance matrices.
mat	A string specifying which matrix to return: "M" (default) for \mathbf{M} and "G" for \mathbf{G}.
...	Arguments passed on to cscov mse If TRUE (default) the residuals used to compute the covariance matrix are not mean-corrected. shrink_fun Shrinkage function of the covariance matrix, shrink_estim (default).

Value

The projection matrix \mathbf{M} (mat = "M") or the mapping matrix \mathbf{G} (mat = "G").

References

Girolimetto, D., Athanasopoulos, G., Di Fonzo, T. and Hyndman, R.J. (2024), Cross-temporal probabilistic forecast reconciliation: Methodological and practical issues. International Journal of Forecasting, 40, 3, 1134-1151. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.ijforecast.2023.10.003")}

See Also

Utilities: FoReco2matrix(), aggts(), balance_hierarchy(), commat(), cstools(), ctprojmat(), cttools(), df2aggmat(), lcmat(), recoinfo(), res2matrix(), shrink_estim(), teprojmat(), tetools(), unbalance_hierarchy()

Examples

# Cross-sectional framework
A <- t(c(1,1)) # Aggregation matrix for Z = X + Y
Mcs <- csprojmat(agg_mat = A, comb = "ols")
Gcs <- csprojmat(agg_mat = A, comb = "ols", mat = "G")

FoReco documentation built on Sept. 14, 2024, 9:07 a.m.