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BUIS for Probabilistic Reconciliation of forecasts via conditioning

Source: R/reconc_BUIS.R
reconc_BUIS.Rd

Uses the Bottom-Up Importance Sampling algorithm to draw samples from the reconciled forecast distribution, obtained via conditioning.

Usage

reconc_BUIS(
  A,
  base_fc,
  in_type,
  distr,
  num_samples = 20000,
  suppress_warnings = FALSE,
  return_upper = TRUE,
  seed = NULL
)

Arguments

A

aggregation matrix (n_upper x n_bottom).

base_fc

A list containing the base_forecasts, see details.

in_type

A string or a list of length n_upper + n_bottom. If it is a list the i-th element is a string with two possible values:

  • 'samples' if the i-th base forecasts are in the form of samples;

  • 'params' if the i-th base forecasts are in the form of estimated parameters.

If it in_type is a string it is assumed that all base forecasts are of the same type.

distr

A string or a list of length n_upper + n_bottom describing the type of base forecasts. If it is a list the i-th element is a string with two possible values:

  • 'continuous' or 'discrete' if in_type[[i]]='samples';

  • 'gaussian', 'poisson' or 'nbinom' if in_type[[i]]='params'.

If distr is a string it is assumed that all distributions are of the same type.

num_samples

Number of samples drawn from the reconciled distribution. This is ignored if bottom_in_type='samples'; in this case, the number of reconciled samples is equal to the number of samples of the base forecasts.

suppress_warnings

Logical. If TRUE, no warnings about effective sample size are triggered. If FALSE, warnings are generated. Default is FALSE. See Details.

return_upper

Logical, whether to return the reconciled parameters for the upper variables (default is TRUE).

seed

Seed for reproducibility.

Value

A list containing the reconciled forecasts. The list has the following named elements:

  • bottom_rec_samples: a matrix (n_bottom x num_samples) containing the reconciled samples for the bottom time series;

  • upper_rec_samples: (only if return_upper = TRUE) a matrix (n_upper x num_samples) containing the reconciled samples for the upper time series.

Details

The parameter base_fc is a list containing n = n_upper + n_bottom elements. The first n_upper elements of the list are the upper base forecasts, in the order given by the rows of A. The elements from n_upper+1 until the end of the list are the bottom base forecasts, in the order given by the columns of A.

The i-th element depends on the values of in_type[[i]] and distr[[i]].

If in_type[[i]]='samples', then base_fc[[i]] is a vector containing samples from the base forecast distribution.

If in_type[[i]]='params', then base_fc[[i]] is a list containing the estimated:

  • mean and sd for the Gaussian base forecast if distr[[i]]='gaussian', see Normal;

  • lambda for the Poisson base forecast if distr[[i]]='poisson', see Poisson;

  • size and prob (or mu) for the negative binomial base forecast if distr[[i]]='nbinom', see NegBinomial.

See the description of the parameters in_type and distr for more details.

Warnings are triggered from the Importance Sampling step if:

  • weights are all zeros, then the upper is ignored during reconciliation;

  • the effective sample size is < 200;

  • the effective sample size is < 1% of the sample size (num_samples if in_type is 'params' or the size of the base forecast if if in_type is 'samples').

Note that warnings are an indication that the base forecasts might have issues. Please check the base forecasts in case of warnings.

References

Zambon, L., Azzimonti, D. & Corani, G. (2024). Efficient probabilistic reconciliation of forecasts for real-valued and count time series. Statistics and Computing 34 (1), 21. doi:10.1007/s11222-023-10343-y .

See also

reconc_gaussian()

Examples


library(bayesRecon)

# Create a minimal hierarchy with 2 bottom and 1 upper variable
rec_mat <- get_reconc_matrices(agg_levels = c(1, 2), h = 2)
A <- rec_mat$A
S <- rec_mat$S


# 1) Gaussian base forecasts

# Set the parameters of the Gaussian base forecast distributions
mu1 <- 2
mu2 <- 4
muY <- 9
mus <- c(muY, mu1, mu2)

sigma1 <- 2
sigma2 <- 2
sigmaY <- 3
sigmas <- c(sigmaY, sigma1, sigma2)

base_fc <- list()
for (i in 1:length(mus)) {
  base_fc[[i]] <- list(mean = mus[[i]], sd = sigmas[[i]])
}


# Sample from the reconciled forecast distribution using the BUIS algorithm
buis <- reconc_BUIS(A, base_fc,
  in_type = "params",
  distr = "gaussian", num_samples = 100000, seed = 42
)

samples_buis <- rbind(buis$upper_rec_samples, buis$bottom_rec_samples)

# In the Gaussian case, the reconciled distribution is still Gaussian and can be
# computed in closed form
Sigma <- diag(sigmas^2) # transform into covariance matrix
analytic_rec <- reconc_gaussian(A,
  base_fc_mean = mus,
  base_fc_cov = Sigma
)

# Compare the reconciled means obtained analytically and via BUIS
print(c(S %*% analytic_rec$bottom_rec_mean))
#> [1] 7.411765 2.705882 4.705882
print(rowMeans(samples_buis))
#> [1] 7.413147 2.707427 4.705720


# 2) Poisson base forecasts

# Set the parameters of the Poisson base forecast distributions
lambda1 <- 2
lambda2 <- 4
lambdaY <- 9
lambdas <- c(lambdaY, lambda1, lambda2)

base_fc <- list()
for (i in 1:length(lambdas)) {
  base_fc[[i]] <- list(lambda = lambdas[i])
}

# Sample from the reconciled forecast distribution using the BUIS algorithm
buis <- reconc_BUIS(A, base_fc,
  in_type = "params",
  distr = "poisson", num_samples = 100000, seed = 42
)
samples_buis <- rbind(buis$upper_rec_samples, buis$bottom_rec_samples)

# Print the reconciled means
print(rowMeans(samples_buis))
#> [1] 7.09171 2.36542 4.72629