mse_f_test: McCracken MSE-F Test for Equal Forecast Accuracy

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McCracken MSE-F Test for Equal Forecast Accuracy

Description

Tests the null hypothesis of equal mean squared forecast error between the (restricted) benchmark and the (unrestricted) alternative nested model, using the MSE-F statistic of McCracken (2007). Under the null, the alternative does not reduce MSFE relative to the benchmark.

Usage

mse_f_test(e1, e2, h = 1L)

Arguments

e1	Numeric vector of forecast errors from the benchmark (restricted) model.
e2	Numeric vector of forecast errors from the alternative (unrestricted) model.
h	Integer; forecast horizon. Default 1.

Details

The MSE-F statistic is:

\text{MSE-F} = (T - h + 1) \cdot \frac{\text{MSFE}_1 - \text{MSFE}_2}{\text{MSFE}_2}

where T is the number of out-of-sample observations and h is the forecast horizon.

Critical values are non-standard and depend on the number of extra regressors in the alternative model (k_2) and on \pi = P/R (out-of-sample size relative to estimation window). See McCracken (2007, Table 1) for asymptotic critical values.

Value

A list with class "mse_f_test" containing:

statistic	The MSE-F test statistic.
msfe1	Mean squared forecast error of the benchmark.
msfe2	Mean squared forecast error of the alternative.
n	Number of out-of-sample observations.
h	Forecast horizon.

References

McCracken, M.W. (2007). Asymptotics for out of sample tests of Granger causality. Journal of Econometrics, 140(2), 719-752.

Clark, T.E. and McCracken, M.W. (2001). Tests of Equal Forecast Accuracy and Encompassing for Nested Models. Journal of Econometrics, 105(1), 85-110.

Examples

set.seed(42)
e1 <- rnorm(100)
e2 <- rnorm(100, sd = 0.9)
mse_f_test(e1, e2)

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