pitHistogram#

Purpose#

Compute and display a PIT histogram for visual calibration assessment.

Format#

counts = pitHistogram(pit_values)#

counts = pitHistogram(pit_values, n_bins)

Parameters:

pit_values (Nx1 vector) – PIT values from pitTest().
n_bins (scalar) – Optional, number of bins. Default = 10.

Returns:

counts (n_bins x 1 vector) – bin counts.

Examples#

new;
library timeseries;

pt = pitTest(sorted_draws, actual, quiet=1);
counts = pitHistogram(pt.pit_values);

// A uniform histogram indicates good calibration
print counts;

Remarks#

A well-calibrated density forecast produces a uniform PIT histogram. Humps indicate underdispersion (too narrow intervals); U-shapes indicate overdispersion. Skewness indicates bias.

Model#

The PIT histogram bins the empirical CDF values \(u_t = \hat{F}_t(y_t)\) into equal-width bins on [0, 1]. Under correct calibration, all bins should have approximately equal height (\(T / n_{\text{bins}}\)). Deviations indicate:

Hump in center: Underdispersion (intervals too narrow — overconfident).
U-shape (high at edges): Overdispersion (intervals too wide — underconfident).
Skewed: Systematic bias in the predictive mean.

References#

Diebold, F.X., T.A. Gunther, and A.S. Tay (1998). “Evaluating density forecasts.” International Economic Review, 39(4), 863-883.

Library#

timeseries

Source#

scoring.src