cslcc {FoReco} | R Documentation |
Level conditional coherent reconciliation for genuine hierarchical/grouped time series
Description
This function implements the cross-sectional forecast reconciliation procedure that extends the original proposal by Hollyman et al. (2021). Level conditional coherent reconciled forecasts are conditional on (i.e., constrained by) the base forecasts of a specific upper level in the hierarchy (exogenous constraints). It also allows handling the linear constraints linking the variables endogenously (Di Fonzo and Girolimetto, 2022). The function can calculate Combined Conditional Coherent (CCC) forecasts as simple averages of Level-Conditional Coherent (LCC) and bottom-up reconciled forecasts, with either endogenous or exogenous constraints.
Usage
cslcc(base, agg_mat, nodes = "auto", comb = "ols", res = NULL, CCC = TRUE,
const = "exogenous", bts = NULL, approach = "proj", nn = NULL,
settings = NULL, ...)
Arguments
base |
A ( |
agg_mat |
A ( |
nodes |
A ( |
comb |
A string specifying the reconciliation method. For a complete list, see cscov. |
res |
An ( |
CCC |
A logical value indicating whether the Combined Conditional Coherent reconciled
forecasts reconciliation should include bottom-up forecasts ( |
const |
A string specifying the reconciliation constraints:
|
bts |
A ( |
approach |
A string specifying the approach used to compute the reconciled forecasts. Options include: |
nn |
A string specifying the algorithm to compute non-negative forecasts:
|
settings |
A list of control parameters.
|
... |
Arguments passed on to
|
Value
A (h \times n
) numeric matrix of cross-sectional reconciled forecasts.
References
Byron, R.P. (1978), The estimation of large social account matrices, Journal of the Royal Statistical Society, Series A, 141, 3, 359-367. doi:10.2307/2344807
Byron, R.P. (1979), Corrigenda: The estimation of large social account matrices, Journal of the Royal Statistical Society, Series A, 142(3), 405. doi:10.2307/2982515
Di Fonzo, T. and Girolimetto, D. (2024), Forecast combination-based forecast reconciliation: Insights and extensions, International Journal of Forecasting, 40(2), 490–514. doi:10.1016/j.ijforecast.2022.07.001
Di Fonzo, T. and Girolimetto, D. (2023b) Spatio-temporal reconciliation of solar forecasts. Solar Energy 251, 13–29. doi:10.1016/j.solener.2023.01.003
Hyndman, R.J., Ahmed, R.A., Athanasopoulos, G. and Shang, H.L. (2011), Optimal combination forecasts for hierarchical time series, Computational Statistics & Data Analysis, 55, 9, 2579-2589. doi:10.1016/j.csda.2011.03.006
Hollyman, R., Petropoulos, F. and Tipping, M.E. (2021), Understanding forecast reconciliation. European Journal of Operational Research, 294, 149–160. doi:10.1016/j.ejor.2021.01.017
Stellato, B., Banjac, G., Goulart, P., Bemporad, A. and Boyd, S. (2020), OSQP: An Operator Splitting solver for Quadratic Programs, Mathematical Programming Computation, 12, 4, 637-672. doi:10.1007/s12532-020-00179-2
See Also
Level conditional coherent reconciliation:
ctlcc()
,
telcc()
Cross-sectional framework:
csboot()
,
csbu()
,
cscov()
,
csmo()
,
csrec()
,
cstd()
,
cstools()
Examples
set.seed(123)
# Aggregation matrix for Z = X + Y, X = XX + XY and Y = YX + YY
A <- matrix(c(1,1,1,1,1,1,0,0,0,0,1,1), 3, byrow = TRUE)
# (2 x 7) base forecasts matrix (simulated)
base <- matrix(rnorm(7*2, mean = c(40, 20, 20, 10, 10, 10, 10)), 2, byrow = TRUE)
# (10 x 7) in-sample residuals matrix (simulated)
res <- matrix(rnorm(n = 7*10), ncol = 7)
# (2 x 7) Naive bottom base forecasts matrix: all forecasts are set equal to 10
naive <- matrix(10, 2, 4)
## EXOGENOUS CONSTRAINTS (Hollyman et al., 2021)
# Level Conditional Coherent (LCC) reconciled forecasts
exo_LC <- cslcc(base = base, agg_mat = A, comb = "wls", bts = naive,
res = res, nodes = "auto", CCC = FALSE)
# Combined Conditional Coherent (CCC) reconciled forecasts
exo_CCC <- cslcc(base = base, agg_mat = A, comb = "wls", bts = naive,
res = res, nodes = "auto", CCC = TRUE)
# Results detailed by level:
# L-1: Level 1 immutable reconciled forecasts for the whole hierarchy
# L-2: Middle-Out reconciled forecasts
# L-3: Bottom-Up reconciled forecasts
info_exo <- recoinfo(exo_CCC, verbose = FALSE)
info_exo$lcc
## ENDOGENOUS CONSTRAINTS (Di Fonzo and Girolimetto, 2024)
# Level Conditional Coherent (LCC) reconciled forecasts
endo_LC <- cslcc(base = base, agg_mat = A, comb = "wls",
res = res, nodes = "auto", CCC = FALSE,
const = "endogenous")
# Combined Conditional Coherent (CCC) reconciled forecasts
endo_CCC <- cslcc(base = base, agg_mat = A, comb = "wls",
res = res, nodes = "auto", CCC = TRUE,
const = "endogenous")
# Results detailed by level:
# L-1: Level 1 reconciled forecasts for L1 + L3 (bottom level)
# L-2: Level 2 reconciled forecasts for L2 + L3 (bottom level)
# L-3: Bottom-Up reconciled forecasts
info_endo <- recoinfo(endo_CCC, verbose = FALSE)
info_endo$lcc