spa_test: Unconditional Superior Predictive Ability (USPA/SPA) Test

In forecastdom: (Un)Conditional Forecast Dominance

Unconditional Superior Predictive Ability (USPA/SPA) Test

Description

Tests the null hypothesis that a benchmark forecasting method has unconditional superior predictive ability over all competing alternatives, using Hansen's (2005) stationary bootstrap approach.

Usage

spa_test(Y, level, B = 5000L, q = 0.25)

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.
level	Significance level (e.g., 0.05).
B	Integer; number of bootstrap replications. Default 5000.
q	Numeric in (0, 1); parameter for the geometric distribution in the stationary bootstrap. Controls the average block length (1/q). Default 0.25 (average block length of 4).

Details

Let d_{j,t} = -Y_{j,t}, so that positive values mean competitor j beats the benchmark. The SPA test statistic is:

T^{SPA} = \max\left(\max_{1 \le j \le J} \frac{\sqrt{n}\, \bar{d}_j}{\hat{\omega}_j}, 0\right)

where \bar{d}_j is the sample mean of d_{j,t} and \hat{\omega}_j^2 is its Newey-West long-run variance.

The null hypothesis is rejected when the benchmark is not superior to all competitors, i.e., some competitor significantly outperforms it.

The bootstrap distribution uses Hansen's (2005) consistent recentring: competitors with \sqrt{n}\, \bar{d}_j / \hat{\omega}_j < -\sqrt{2 \log \log n} are treated as clearly inferior and recentred at zero instead of \bar{d}_j, so they do not inflate the critical value.

Value

A list with class "spa_test" containing:

statistic	The SPA test statistic (consistent).
pvalue	Bootstrap p-value.
reject	Logical; whether the null is rejected.
level	Significance level used.
d_bar	Sample mean of loss differentials for each competitor.
n	Number of observations.
J	Number of competitors.
B	Number of bootstrap replications.

References

Hansen, P.R. (2005). A Test for Superior Predictive Ability. Journal of Business & Economic Statistics, 23(4), 365-380.

White, H. (2000). A Reality Check for Data Snooping. Econometrica, 68(5), 1097-1126.

Examples

sim <- do_sim(J = 3, n = 250, a = 1, c = 0, rho_u = 0.4)
spa_test(sim$Y, level = 0.05, B = 500)

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