cscov: Cross-sectional covariance matrix approximation

In FoReco: Forecast Reconciliation

Cross-sectional covariance matrix approximation

Description

This function provides an approximation of the cross-sectional base forecasts errors covariance matrix using different reconciliation methods (see Wickramasuriya et al., 2019 and Di Fonzo and Girolimetto, 2023).

Usage

cscov(comb = "ols", n = NULL, agg_mat = NULL, res, mse = TRUE,
      shrink_fun = shrink_estim, ...)

Arguments

comb	A string specifying the reconciliation method. Ordinary least squares: "ols" (default) - identity error covariance matrix. Weighted least squares: "str" - structural variances. "wls" - series variances (uses res). Generalized least squares: "shr"/"sam" - shrunk/sample covariance (uses res).
n	Number of variables (n = n_a + n_b).
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.
res	An (N \times n) optional numeric matrix containing the in-sample residuals. This matrix is used to compute some covariance matrices.
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).
...	Not used.

Value

A (n \times n) symmetric positive (semi-)definite matrix.

References

Di Fonzo, T. and Girolimetto, D. (2023), Cross-temporal forecast reconciliation: Optimal combination method and heuristic alternatives, International Journal of Forecasting, 39, 1, 39-57. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.ijforecast.2021.08.004")}

Wickramasuriya, S.L., Athanasopoulos, G. and Hyndman, R.J. (2019), Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization, Journal of the American Statistical Association, 114, 526, 804-819. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.2018.1448825")}

See Also

Cross-sectional framework: csboot(), csbu(), cslcc(), csmo(), csrec(), cstd(), cstools()

Examples

# Aggregation matrix for Z = X + Y
A <- t(c(1,1))
# (10 x 3) in-sample residuals matrix (simulated)
res <- t(matrix(rnorm(n = 30), nrow = 3))

cov1 <- cscov("ols", n = 3)          # OLS methods
cov2 <- cscov("str", agg_mat = A)   # STR methods
cov3 <- cscov("wls", res = res)      # WLS methods
cov4 <- cscov("shr", res = res)      # SHR methods
cov5 <- cscov("sam", res = res)      # SAM methods

# Custom covariance matrix
cscov.ols2 <- function(comb, x) diag(x)
cscov(comb = "ols2", x = 3) # == cscov("ols", n = 3)

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