## ----include = FALSE----------------------------------------------------------
knitr::opts_chunk$set(
  collapse = TRUE,
  comment  = "#>",
  fig.width  = 7,
  fig.height = 4
)

## ----setup, message = FALSE---------------------------------------------------
library(forecastdom)
data(hl2005)

n <- length(hl2005$date)
J <- ncol(hl2005$forecasts)
sprintf("Sample: %s to %s (%d trading days), %d forecast models.",
        hl2005$date[1], hl2005$date[n], n, J)

## ----setup-losses-------------------------------------------------------------
b <- hl2005$garch11_idx

build_Y <- function(rv) {

  L <- (hl2005$forecasts - rv) ^ 2
  L[, -b] - L[, b]

}

Y <- build_Y(hl2005$rv) # primary RV proxy (5-min linear)
dim(Y)

cat("Competitors with lower MSE than GARCH(1,1):",
    sum(colMeans(Y) < 0), "of", ncol(Y), "\n")

## ----primary-spa--------------------------------------------------------------
set.seed(20260512)

r <- spa_test(Y, level = 0.05, B = 5000L, q = 0.25)

r

## ----proxy-grid---------------------------------------------------------------
proxies <- colnames(hl2005$rv_proxies)

tab <- do.call(rbind, lapply(proxies, function(p) {

  set.seed(20260512)

  r <- spa_test(build_Y(hl2005$rv_proxies[, p]), level = 0.05, B = 5000L, q = 0.25)

  data.frame(proxy = p,
             T_SPA   = unname(r$statistic),
             pvalue  = unname(r$pvalue),
             reject  = unname(r$reject),
             n_beat  = sum(colMeans(build_Y(hl2005$rv_proxies[, p])) < 0))

}))

knitr::kable(
  tab, digits = 3, row.names = FALSE,
  col.names = c("Proxy", "$T^{SPA}$", "$p$-value",
                "Reject", "$n_{\\text{beat}}$"))

## ----top10--------------------------------------------------------------------
d_bar <- colMeans(Y)
top10_idx <- order(d_bar)[1:10]

data.frame(rank = 1:10,
           competitor_col = (1:J)[-b][top10_idx],
           mean_loss_diff = round(d_bar[top10_idx], 3))