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 qmatrix of instruments (conditioning variables) observed at the time of the forecast. IfNULL(default), uses a constant and the lagged loss differential.- loss
Character; loss function.
"SE"for squared error (default),"AE"for absolute error.
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.
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.
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)
#>
#> ╭────────────────────────────────────────────────────╮
#> │ Conditional Equal Predictive Ability Test │
#> │ (Giacomini and White, 2006) │
#> ├────────────────────────────────────────────────────┤
#> │ H0: Equal conditional predictive ability │
#> │ H1: Methods differ conditionally │
#> ├┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┤
#> │ Test Results: │
#> │ Wald statistic: 3.6214 │
#> │ P-value: 0.1635 │
#> ├┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┤
#> │ Details: │
#> │ Observations (n): 199 │
#> │ Instruments (q): 2 │
#> │ Loss function: SE │
#> │ Reference distribution: Chi-sq(2) │
#> ╰────────────────────────────────────────────────────╯
#>