FoReco (version 1.2.0)

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, tew = "sum", res = NULL, mse = TRUE,
      shrink_fun = shrink_estim, ...)

Value

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

Arguments

comb

A string specifying the covariance approximation method.

• For ordinary least squares reconciliation:

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

• For weighted least squares reconciliation:

  • "str" - structural variances.

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

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

• For generalized least squares (uses res) reconciliation:

  • "acov" - series auto-covariance.

  • "strar1" - structural Markov covariance.

  • "sar1" - series Markov covariance.

  • "har1" - hierarchy Markov covariance.

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

• Others (no for reconciliation):

  • "bu" - bottom-up 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 \(m\).

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).

res

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

mse

If TRUE (default) the errors 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. (2023a), 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(), temvn(), terec(), tesmp(), tetd(), tetools()

Examples

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

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

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