cspa_test: Conditional Superior Predictive Ability (CSPA) Test

In forecastdom: (Un)Conditional Forecast Dominance

Conditional Superior Predictive Ability (CSPA) Test

Description

Tests the null hypothesis that a benchmark forecasting method has conditional superior predictive ability over competing alternatives, uniformly across all conditioning states. Based on Li, Liao, and Quaedvlieg (2022).

Usage

cspa_test(Y, X, level, trim = 0, prewhiten = -1L, preselect = TRUE, R = 10000L)

Arguments

Y	An n x J matrix of loss differentials with respect to the benchmark. Positive values indicate the benchmark outperforms competitor j in period t.
X	An n x 1 numeric vector of the conditioning variable.
level	Significance level (e.g., 0.05).
trim	Trim observations where the conditioning variable exceeds this many standard deviations from the mean. Use 0 (default) for no trimming.
prewhiten	Order of pre-whitening VAR for HAC estimation. Use 0 for standard Newey-West, or -1 (default) for AIC-based lag selection.
preselect	Logical; perform adaptive inequality selection? Default TRUE.
R	Integer; number of bootstrap replications for critical value computation. Default 10000.

Value

A list with class "cspa_test" containing:

theta	Infimum of the upper confidence bound. Negative values lead to rejection of the null.
pvalue	P-value for the test.
reject	Logical; whether the null is rejected at the given level.
level	Significance level used.
h_hat	Estimated conditional mean functions (n x J matrix).
sigma_jx	Estimated standard deviations (J x n matrix).
kp	Critical value from adaptive inequality selection.
Vhat	Logical matrix indicating selected (j, x) pairs.
X	Conditioning variable (after trimming).
Y	Loss differentials (after trimming).
K	Number of series terms used.
prewhiten_order	Pre-whitening lag order actually used.

References

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

Examples

sim <- do_sim(J = 3, n = 250, a = 1, c = 0, rho_u = 0.4)
result <- cspa_test(sim$Y, sim$X, level = 0.05, trim = 2, R = 500L)
print(result)

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