Tests whether an alternative (unrestricted) model has superior out-of-sample predictive ability relative to a benchmark (restricted) model, using the MSFE-adjusted statistic of Clark and West (2007). Also computes the out-of-sample \(R^2_{OS}\) statistic.
Value
A list with class "cw_test" containing:
- statistic
The Clark-West t-statistic.
- pvalue
One-sided p-value (H1: alternative is better).
- r2os
Out-of-sample \(R^2_{OS}\) in percent.
- n
Number of observations.
Details
The MSFE-adjusted series is defined as: $$\hat{f}_t = e_{1,t}^2 - \left(e_{2,t}^2 - (f_{1,t} - f_{2,t})^2\right)$$ The test regresses \(\hat{f}_t\) on a constant and uses the resulting t-statistic, compared to a standard normal distribution (one-sided).
References
Clark, T.E. and West, K.D. (2007). Approximately Normal Tests for Equal Predictive Accuracy in Nested Models. Journal of Econometrics, 138(1), 291-311.
Examples
set.seed(42)
n <- 200
actual <- rnorm(n)
f1 <- actual + rnorm(n, sd = 0.5)
f2 <- actual + rnorm(n, sd = 0.4)
e1 <- actual - f1
e2 <- actual - f2
cw_test(e1, e2, f1, f2)
#>
#> ╭────────────────────────────────────────────────────╮
#> │ Clark-West Test (2007) │
#> ├────────────────────────────────────────────────────┤
#> │ H0: Benchmark MSFE <= Alternative MSFE │
#> │ H1: Alternative model is superior (R2OS > 0) │
#> ├┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┤
#> │ Test Results: │
#> │ CW statistic: 9.7491 │
#> │ P-value (one-sided): 0.0000 │
#> │ R2OS (%): 22.45 │
#> ├┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┄┤
#> │ Details: │
#> │ Observations (n): 200 │
#> │ Reference distribution: N(0,1) │
#> ╰────────────────────────────────────────────────────╯
#>