predictive_moments: Analytical computation of predictive moments for an 'hhh4'...

In jbracher/hhh4addon: Extensions to endemic-epidemic timeseries modeling from package surveillance

Analytical computation of predictive moments for an hhh4 model

Description

This functions calculates the predictive mean vector and covariance matrix for a path forecast from an hhh4 model.

Usage

predictive_moments(
  hhh4Obj,
  t_condition,
  lgt,
  return_Sigma = FALSE,
  return_cov_array = FALSE,
  return_mu_decomposed = FALSE,
  return_M = FALSE
)

Arguments

hhh4Obj	an hhh4 object
t_condition	the index of the week on which to condition the path forecast, i.e. an integer between 1 and nrow(hhh4Obj$stsObj@observed). If you need forecasts beyond the end of your observed time series you need to artificially prolong the sts object used by adding NA values to the end.
lgt	the length of the path forecast, i.e. 52 for forecasting an entire season when using weekly data
return_Sigma	logical: should the entire variance-covariance matrix of the forecast be returned? defaults to FALSE in order to save storage.
return_cov_array	logical: should an array with week-wise covariance matrices be returned?
return_mu_decomposed	logical: should an array with the predictive means decomposed into the different components be returned?
return_M	logical: should the matrix M containing the predictive first and (un-centered) second moments be returned?

Value

An object of class predictive_moments_hhh4 containing the following components:

• mu_matrix A matrix containing the predictive means. Each row corresponds to a time period and each column to a unit.

• var_matrix A matrix containing the predictive variances.

• cov_array An array containing time period-wise variance-covariance matrices.

• mu_vector as mu_matrix, but flattened into a vector.

• Sigma a large covariance matrix for all elements of the prediction (corresponding to mu_vector)

• M a matrix containing predictive means and (un-centered) second moments, specifically E(c(1, X) shall be forecasted. Important in the internal calculation, accessible mainly for de-bugging purposes.

• mu_decomposed an array with the same number of rows and columns as mu_matrix, but three layers corresponding to the contributions of the three components to the means

• start the index (in the original sts object) of the first time period of the prediction

• freq the length of a cycle

• n_units the number of units covered in the prediction

• timepoints the timepoints covered by the prediction etc.

• timepoints as timepoints, but calendar time rather than indices

• condition A matrix containing the realizations for the conditioning time period (or periods)

• realizations_matrix A matrix containing the realizations that have materialized in the period covered by the prediction.

• type "predictive"; to distinguish from stationary moments.

• has_temporal_structure does the object still have the original temporal structure? can be set to FALSE when aggregated using aggregate_prediction.

Examples

data("salmonella.agona")
# convert old "disProg" to new "sts" data class:
salmonella <- disProg2sts(salmonella.agona)
control_salmonella <- list(end = list(f = addSeason2formula(~ 1), lag = 1),
                           ar = list(f = addSeason2formula(~ 1), lag = 1),
                           family = "NegBinM", subset = 6:250)
fit_salmonella <- hhh4_lag(salmonella, control_salmonella) # fit model
# obtain prediction:
pred_mom <- predictive_moments(fit_salmonella, t_condition = 250, lgt = 52)
plot(fit_salmonella)
fanplot_prediction(pred_mom, add = TRUE) # add fan plot

jbracher/hhh4addon documentation built on Aug. 29, 2024, 9:53 a.m.