DM rejection frequency
—Monte Carlo SE —Extreme observations over brief time periods can reduce the power of the Diebold–Mariano (DM) test. When the instability window is known in advance, the winsorised DM* test recovers the usual DM test’s power.
01 · Monte Carlo study
Change the DGP
The simulated loss differential is dt = κ + θIt(τ;m) + ut, with ut = φut−1 + εt. The instability window is treated as known in advance.
DM* rejection frequency
—Monte Carlo SE —DM* − DM
—Critical value —One simulated path
Raw and winsorised loss differential
Raw Winsorised
The declared shock window will be shaded after the simulation runs.
Interpretation
Run the experiment to obtain an interpretation of this design.
02 · Your data
Test two forecast series
Upload outcomes and two forecasts, two forecast-error series, or a pre-computed loss differential. The file stays in your browser.
CSV input
Load data
Accepted column sets: outcome, forecast_a, forecast_b; error_a, error_b; or loss_diff. A date column is optional.
No data loaded.
Evaluation settings
Declare the instability window
Load a file, then specify a window independently of the desired result.
Ordinary DM statistic
—Decision —Winsorised DM* statistic
—Decision —Observations modified
—Stable range —Diagnostic
Loss differential
Raw and winsorised series will appear here.
Estimand warning
What DM* means
DM* tests equal predictive ability outside the pre-specified instability window. It is not evidence about relative performance inside that window.
Sample size—
Mean loss differential—
Winsorised mean—
Critical value—
03 · Methodology
The winsorised DM test
The ordinary and winsorised DM statistics use the same Bartlett long-run variance estimate. Only the series of loss differentials changes.
Form the loss differential
dt = L(eA,t) − L(eB,t). Squared and absolute loss are available.
Cap the declared window
Each observation inside the window is capped at the minimum or maximum observed outside it.
Estimate long-run variance
The long-run variance is estimated using Bartlett weights:
σ̂2 = γ̂0 + 2∑j=1M [(M − j)/M] γ̂j.
Perform the test
At the 5% level, reject equal predictive ability when the absolute DM* statistic exceeds the selected critical value.
Paper empirical application
Results
SPF application: DM = 1.458, DM* = 6.147, and the 5% fixed-smoothing critical value is 2.261. SPF MSE is 4.51, compared with 31.17 for the zero-growth benchmark.