reconc_TDcond {bayesRecon} | R Documentation |
Probabilistic forecast reconciliation of mixed hierarchies via top-down conditioning
Description
Uses the top-down conditioning algorithm to draw samples from the reconciled forecast distribution. Reconciliation is performed in two steps: first, the upper base forecasts are reconciled via conditioning, using only the hierarchical constraints between the upper variables; then, the bottom distributions are updated via a probabilistic top-down procedure.
Usage
reconc_TDcond(
S,
fc_bottom,
fc_upper,
bottom_in_type = "pmf",
distr = NULL,
num_samples = 20000,
return_type = "pmf",
suppress_warnings = FALSE,
seed = NULL
)
Arguments
S |
Summing matrix (n x n_bottom). |
fc_bottom |
A list containing the bottom base forecasts, see details. |
fc_upper |
A list containing the upper base forecasts, see details. |
bottom_in_type |
A string with three possible values:
|
distr |
A string describing the type of bottom base forecasts ('poisson' or 'nbinom'). This is only used if |
num_samples |
Number of samples drawn from the reconciled distribution.
This is ignored if |
return_type |
The return type of the reconciled distributions. A string with three possible values:
|
suppress_warnings |
Logical. If |
seed |
Seed for reproducibility. |
Details
The base bottom forecasts fc_bottom
must be a list of length n_bottom, where each element is either
a PMF object (see details below), if
bottom_in_type='pmf'
;a vector of samples, if
bottom_in_type='samples'
;a list of parameters, if
bottom_in_type='params'
:lambda for the Poisson base forecast if
distr
='poisson', see Poisson;size and prob (or mu) for the negative binomial base forecast if
distr
='nbinom', see NegBinomial.
The base upper forecasts fc_upper
must be a list containing the parameters of
the multivariate Gaussian distribution of the upper forecasts.
The list must contain only the named elements mu
(vector of length n_upper)
and Sigma
(n_upper x n_upper matrix)
A PMF object is a numerical vector containing the probability mass function of a discrete distribution. Each element corresponds to the probability of the integers from 0 to the last value of the support. See also PMF.get_mean, PMF.get_var, PMF.sample, PMF.get_quantile, PMF.summary for functions that handle PMF objects.
If some of the reconciled upper samples lie outside the support of the bottom-up distribution, those samples are discarded and a warning is triggered. The warning reports the percentage of samples kept.
Value
A list containing the reconciled forecasts. The list has the following named elements:
-
bottom_reconciled
: a list containing the pmf, the samples (matrix n_bottom xnum_samples
) or both, depending on the value ofreturn_type
; -
upper_reconciled
: a list containing the pmf, the samples (matrix n_upper xnum_samples
) or both, depending on the value ofreturn_type
.
References
Corani, G., Azzimonti, D., Augusto, J.P.S.C., Zaffalon, M. (2021). Probabilistic Reconciliation of Hierarchical Forecast via Bayes' Rule. ECML PKDD 2020. Lecture Notes in Computer Science, vol 12459. doi:10.1007/978-3-030-67664-3_13.
Zambon, L., Agosto, A., Giudici, P., Corani, G. (2024). Properties of the reconciled distributions for Gaussian and count forecasts. International Journal of Forecasting (in press). doi:10.1016/j.ijforecast.2023.12.004.
Zambon, L., Azzimonti, D., Rubattu, N., Corani, G. (2024). Probabilistic reconciliation of mixed-type hierarchical time series. The 40th Conference on Uncertainty in Artificial Intelligence, accepted.
See Also
reconc_MixCond()
, reconc_BUIS()
Examples
library(bayesRecon)
# Consider a simple hierarchy with two bottom and one upper
A <- matrix(c(1,1),nrow=1)
S <- rbind(A,diag(nrow=2))
# The bottom forecasts are Poisson with lambda=15
lambda <- 15
n_tot <- 60
fc_bottom <- list()
fc_bottom[[1]] <- apply(matrix(seq(0,n_tot)),MARGIN=1,FUN=function(x) dpois(x,lambda=lambda))
fc_bottom[[2]] <- apply(matrix(seq(0,n_tot)),MARGIN=1,FUN=function(x) dpois(x,lambda=lambda))
# The upper forecast is a Normal with mean 40 and std 5
fc_upper<- list(mu=40, Sigma=matrix(c(5^2)))
# We can reconcile with reconc_TDcond
res.TDcond <- reconc_TDcond(S, fc_bottom, fc_upper)
# Note that the bottom distributions are shifted to the right
PMF.summary(res.TDcond$bottom_reconciled$pmf[[1]])
PMF.summary(fc_bottom[[1]])
PMF.summary(res.TDcond$bottom_reconciled$pmf[[2]])
PMF.summary(fc_bottom[[2]])
# The upper distribution remains similar
PMF.summary(res.TDcond$upper_reconciled$pmf[[1]])
PMF.get_var(res.TDcond$upper_reconciled$pmf[[1]])