reconc_MCMC {bayesRecon}

MCMC for Probabilistic Reconciliation of forecasts via conditioning

Description

Uses Markov Chain Monte Carlo algorithm to draw samples from the reconciled forecast distribution, which is obtained via conditioning.

This is a bare-bones implementation of the Metropolis-Hastings algorithm, we suggest the usage of tools to check the convergence. The function only works with Poisson or Negative Binomial base forecasts.

The function reconc_BUIS() is generally faster on most hierarchies.

Usage

reconc_MCMC(
  S,
  base_forecasts,
  distr,
  num_samples = 10000,
  tuning_int = 100,
  init_scale = 1,
  burn_in = 1000,
  seed = NULL
)

Arguments

S

summing matrix (n x n_bottom).

base_forecasts

list of the parameters of the base forecast distributions, see details.

distr

a string describing the type of predictive distribution.

num_samples

number of samples to draw using MCMC.

tuning_int

number of iterations between scale updates of the proposal.

init_scale

initial scale of the proposal.

burn_in

number of initial samples to be discarded.

seed

seed for reproducibility.

Details

The parameter base_forecast is a list containing n elements. Each element is a list containing the estimated:

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

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

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

The order of the base_forecast list is given by the order of the time series in the summing matrix.

Value

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

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

• upper_reconciled_samples: a matrix (n_upper x num_samples) containing reconciled samples for the upper time series;

• reconciled_samples: a matrix (n x num_samples) containing the reconciled samples for all time series.

References

Corani, G., Azzimonti, D., Rubattu, N. (2024). Probabilistic reconciliation of count time series. International Journal of Forecasting 40 (2), 457-469. doi:10.1016/j.ijforecast.2023.04.003.

See Also

reconc_BUIS()

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)
S <- rec_mat$S

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

base_forecasts = list()
for (i in 1:nrow(S)) {
 base_forecasts[[i]] = list(lambda = lambdas[i])
}

#Sample from the reconciled forecast distribution using MCMC
mcmc = reconc_MCMC(S, base_forecasts, distr = "poisson",
                  num_samples = 30000, seed = 42)
samples_mcmc <- mcmc$reconciled_samples

#Compare the reconciled means with those obtained via BUIS
buis = reconc_BUIS(S, base_forecasts, in_type="params",
                   distr="poisson", num_samples=100000, seed=42)
samples_buis <- buis$reconciled_samples

print(rowMeans(samples_mcmc))
print(rowMeans(samples_buis))