skfolio.metrics.qlike_loss#

skfolio.metrics.qlike_loss(returns, forecast_variance)[source]#

QLIKE loss for univariate variance forecasts.

\[\text{QLIKE} = \frac{1}{n} \sum_{t=1}^{n} \left( \log(\sigma_t^2) + \frac{r_t^2}{\sigma_t^2} \right)\]

Lower values are better. For numerical stability, forecast variances are clipped below by a small positive constant before evaluating the score.

In financial time series, QLIKE is often used as a comparative score when returns are heavy-tailed and realized variance is only an imperfect proxy for latent volatility.

Parameters:

returnsarray-like of shape (n_observations,): Realized returns.
forecast_variancearray-like of shape (n_observations,): Forecast variances for the same timestamps, expressed in squared return units.

Returns:

float: Mean QLIKE loss. Lower values are better; in expectation, the loss is minimized by the true conditional variance forecast.