csms: Confidence Set for the Most Superior (CSMS) Forecasting...

In forecastdom: (Un)Conditional Forecast Dominance

Confidence Set for the Most Superior (CSMS) Forecasting Method

Description

Constructs the confidence set for the most superior forecasting method by inverting the CSPA test, as described in Section 2.3 of Li, Liao, and Quaedvlieg (2022). The set contains all methods j for which the CSPA null hypothesis (with j as benchmark) is not rejected.

Usage

csms(
  losses,
  X,
  level,
  trim = 0,
  prewhiten = -1L,
  preselect = TRUE,
  R = 10000L,
  method_names = NULL
)

Arguments

losses	An n x (J+1) matrix where each column contains the loss series for a forecasting method. All methods are treated symmetrically (no pre-specified benchmark).
X	An n x 1 numeric vector of the conditioning variable.
level	Significance level (e.g., 0.05).
trim	Trimming parameter (standard deviations). Default 0.
prewhiten	Pre-whitening order. Default -1 (AIC).
preselect	Logical; adaptive inequality selection. Default TRUE.
R	Integer; Gaussian process replications. Default 10000.
method_names	Optional character vector of method names. If NULL, uses "M1", "M2", ....

Details

For each method j in 0, ..., J, the CSPA test is applied with j as the benchmark. The confidence set is:

\widehat{\mathcal{M}}_{n,1-\alpha} = \{0 \le j \le J : \text{CSPA test with } j \text{ as benchmark does not reject}\}

Value

A list with class "csms" containing:

in_set	Logical vector; which methods are in the confidence set.
set_members	Names of methods in the confidence set.
theta	Theta values for each method as benchmark.
pvalues	P-values for each method as benchmark.
method_names	Names of all methods.
level	Significance level.
n_methods	Total number of methods.

References

Li, J., Liao, Z., and Quaedvlieg, R. (2022). Conditional Superior Predictive Ability. Review of Economic Studies, 89(2), 843-875.

Examples

set.seed(42)
n <- 300
X <- arima.sim(list(ar = 0.5), n = n, sd = sqrt(0.75))
losses <- matrix(rnorm(n * 4), n, 4)
csms(losses, X, level = 0.05, trim = 2, R = 500L)

forecastdom documentation built on Nov. 2, 2026, 1:10 a.m.