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

# \donttest{
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)
#> 
#> ╭────────────────────────────────────────────────────╮
#> │      Conditional Superior Predictive Ability       │
#> │          (Li, Liao, and Quaedvlieg, 2022)          │
#> ├────────────────────────────────────────────────────┤
#> │ H0: Benchmark weakly dominates all competitors     │
#> │     conditionally, uniformly across all states     │
#> │ H1: Some competitor outperforms the benchmark      │
#> │     in certain conditioning states                 │
#> ├┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┤
#> │ Test Results:                                      │
#> │  Theta: 0.3174                                     │
#> │  P-value: 0.8180                                   │
#> │  Significance level: 0.0500                        │
#> │  Decision: Not rejected                            │
#> ├┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┤
#> │ Estimation Details:                                │
#> │  Observations (n): 240                             │
#> │  Competitors (J): 3                                │
#> │  Series terms (K): 4                               │
#> │  HAC lag order: 1 (pre-whitened)                   │
#> │  Selected (j,x) pairs: 720 / 720 (100.0%)          │
#> ╰────────────────────────────────────────────────────╯
#> 
# }