Replicate the thief package

Daniele Girolimetto

2024-08-16

Introduction

The dataset AEdemand in the thief package is used to show how to get the same results with FoReco. In particular, we take the weekly data of Accident and Emergency demand in the UK, AEdemand, from 1 January 2011 to 31 December 2014.

library(FoReco)
library(thief)

extract_thief <- function(x){
  out <- NULL
  for(i in length(x):1) {
    out <- c(out, x[[i]]$mean)
  }
  return(out)
}

Base forecasts

dataset <- window(AEdemand[, 12], start = c(2011, 1), end = c(2014, 52))
data <- tsaggregates(dataset)
# Base forecasts
fc_obj <- list()
for (i in 1:5) {
  fc_obj[[i]] <- forecast(auto.arima(data[[i]]))
}
fc_obj[[6]] <- forecast(auto.arima(data[[6]]), h = 2)
# Base forecasts vector
base <- NULL
for (i in 6:1) {
  base <- c(base, fc_obj[[i]]$mean)
}
# Residual vector
res <- NULL
for (i in 6:1) {
  res <- c(res, fc_obj[[i]]$residuals)
}

Comparisons

# Tollerance setting
tol <- 1e-7

## Bottom-up
thief_bu <- reconcilethief(fc_obj, comb="bu")
FoReco_bu <- tebu(fc_obj[[1]]$mean, agg_order = 52)
sum(abs(FoReco_bu - extract_thief(thief_bu)) > tol)
#> [1] 0

## Ordinary least squares (identity error covariance matrix)
thief_ols <- reconcilethief(fc_obj, comb="ols")
FoReco_ols <- terec(base, 52, comb = "ols")
sum(abs(FoReco_ols - extract_thief(thief_ols)) > tol)
#> [1] 0

## Weighted least squares (structural variances)
thief_str <- reconcilethief(fc_obj, comb="struc")
FoReco_str <- terec(base, 52, comb = "str")
sum(abs(FoReco_str - extract_thief(thief_str)) > tol)
#> [1] 0

## Generalized least squares (shrunk covariance matrix)
thief_shr <- reconcilethief(fc_obj, comb="shr")
FoReco_shr <- terec(base, 52, comb = "shr", res = res)
sum(abs(FoReco_shr - extract_thief(thief_shr)) > tol)
#> [1] 0