FoReco (version 1.0.0)

tecov: Temporal covariance matrix approximation

Description

This function provides an approximation of the temporal base forecasts errors covariance matrix using different reconciliation methods (see Di Fonzo and Girolimetto, 2023).

Usage

tecov(comb, agg_order = NULL, res = NULL, tew = "sum",
      mse = TRUE, shrink_fun = shrink_estim, ...)

Value

A (\((k^\ast+m) \times (k^\ast+m)\)) symmetric matrix.

Arguments

comb

A string specifying the reconciliation method.

• Ordinary least squares:

  • "ols" (default) - identity error covariance.

• Weighted least squares:

  • "str" - structural variances.

  • "wlsh" - hierarchy variances (uses res).

  • "wlsv" - series variances (uses res).

• Generalized least squares (uses res):

  • "acov" - series auto-covariance.

  • "strar1" - structural Markov covariance.

  • "sar1" - series Markov covariance.

  • "har1" - hierarchy Markov covariance.

  • "shr"/"sam" - shrunk/sample covariance.

agg_order

Highest available sampling frequency per seasonal cycle (max. order of temporal aggregation, \(m\)), or a vector representing a subset of \(p\) factors of \(m\).

res

A (\(N(k^\ast+m) \times 1\)) optional numeric vector containing the in-sample residuals at all the temporal frequencies ordered from the lowest frequency to the highest frequency. This vector is used to compute come covariance matrices.

tew

A string specifying the type of temporal aggregation. Options include: "sum" (simple summation, default), "avg" (average), "first" (first value of the period), and "last" (last value of the period).

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.

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. tools:::Rd_expr_doi("10.1016/j.ijforecast.2021.08.004")

See Also

Temporal framework: teboot(), tebu(), telcc(), temo(), terec(), tetd(), tetools()

Examples

# (7 x 70) in-sample residuals matrix (simulated), agg_order = 4
res <- rnorm(70)

cov1 <- tecov("ols", agg_order = 4)                 # OLS methods
cov2 <- tecov("str", agg_order = 4)                 # STRC methods
cov3 <- tecov("wlsv", agg_order = 4, res = res)     # WLSv methods
cov4 <- tecov("wlsh", agg_order = 4, res = res)     # WLSh methods
cov5 <- tecov("acov", agg_order = 4, res = res)     # ACOV methods
cov6 <- tecov("strar1", agg_order = 4, res = res)   # STRAR1 methods
cov7 <- tecov("har1", agg_order = 4, res = res)     # HAR1 methods
cov8 <- tecov("sar1", agg_order = 4, res = res)     # SAR1 methods
cov9 <- tecov("shr", agg_order = 4, res = res)      # SHR methods
cov10 <- tecov("sam", agg_order = 4, res = res)     # SAM methods

# Custom covariance matrix
tecov.ols2 <- function(comb, x) diag(x)
tecov(comb = "ols2", x = 7) # == tecov("ols", agg_order = 4)