This function computes the matrices required for the optimal coherent forecast combination csocc, as described in Girolimetto and Di Fonzo (2024). These matrices serve as the foundation for building forecasts that effectively combines the individual information from multiple experts while ensuring coherence across the variables.
Usage
occmat(agg_mat, cons_mat, p = NULL, matNA = NULL,
comb = "ols", res = NULL, approach = "proj", ...)Arguments
- agg_mat
A (\(n_u \times n_b\)) numeric matrix representing the cross-sectional aggregation matrix, mapping the \(n_b\) bottom-level (free) variables into the \(n_u\) upper (constrained) variables.
- cons_mat
A (\(n_u \times n\)) numeric matrix representing the cross-sectional zero constraints: each row represents a constraint equation, and each column represents a variable. The matrix can be of full rank, meaning the rows are linearly independent, but this is not a strict requirement, as the function allows for redundancy in the constraints.
- p
Total number of experts, \(p\).
- matNA
A (\(n \times p\)) matrix consisting of 0s and 1s, where each element indicates whether expert \(j\) (column) has provided a forecast for variable \(i\) (row). If expert \(j\) has provided a forecast for variable \(i\), the corresponding element \((i,j)\) is 1; otherwise, it is 0.
- comb
A string specifying the reconciliation method. For details, see cscov.
- res
A list of \(p\) numeric (\(N \times n\)) matrix containing the in-sample residuals. This input is used to compute some covariance matrices.
- approach
A string specifying the approach used to compute the reconciled forecasts. Options include:
"
proj" (default): zero-constrained projection approach."
strc": structural approach.
- ...
Arguments passed on to cscov.
Value
A list of matrices:
- M
Projection matrix.
- Omega
Matrix of the combination weights of the optimal linear multi-task forecast combination.
- W
Forecast error covariance matrix of the base forecasts.
- Wc
Forecast error covariance matrix of the combined forecasts.
- Wtilde
Forecast error covariance matrix of the reconciled combined forecasts.
- K
Matrix that replicates a vector (see Girolimetto and Di Fonzo, 2024).