gw_test: Conditional Equal Predictive Ability (CEPA) Test

In forecastdom: (Un)Conditional Forecast Dominance

Conditional Equal Predictive Ability (CEPA) Test

Description

Tests the null hypothesis of conditional equal predictive ability using the Giacomini and White (2006) approach. The test checks whether loss differentials are conditionally mean-zero given an information set, using a finite set of instruments.

Usage

gw_test(e1, e2, instruments = NULL, loss = c("SE", "AE"))

Arguments

e1	Numeric vector of forecast errors from model 1 (benchmark).
e2	Numeric vector of forecast errors from model 2 (competitor).
instruments	An n x q matrix of instruments (conditioning variables) observed at the time of the forecast. If NULL (default), uses a constant and the lagged loss differential.
loss	Character; loss function. "SE" for squared error (default), "AE" for absolute error.

Details

The test is based on the unconditional moment conditions implied by the CEPA null hypothesis:

E[d_t \cdot W_t] = 0

where d_t is the loss differential and W_t is a vector of instruments measurable with respect to the conditioning information set.

The test statistic follows a chi-squared distribution with q degrees of freedom, where q is the number of instruments.

Value

A list with class "gw_test" containing:

statistic	The Wald test statistic.
pvalue	P-value from the chi-squared distribution.
df	Degrees of freedom (number of instruments).
n	Number of observations used.
loss	Loss function used.

References

Giacomini, R. and White, H. (2006). Tests of Conditional Predictive Ability. Econometrica, 74(6), 1545-1578.

Examples

set.seed(42)
e1 <- rnorm(200)
e2 <- rnorm(200, sd = 0.9)
gw_test(e1, e2)

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