Conditional Superior Predictive Ability (CSPA) Test

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

if (FALSE) { # \dontrun{
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)
print(result)
} # }