The polar cap (PC) index is a measure of the high-latitude geomagnetic disturbances due to Hall and field-aligned currents. The index is well correlated with the auroral electrojet AL and AU indices (correlation with the PC index is 76% and 66%, resp.). Here we obtain several types of data-based models that relate the PC to the AL and AU indices in the wintertime, when the ionospheric conductivity is mostly due to the precipitating particles of the field-aligned currents. The new models predict AL and AU from PC with correlations much higher than those found by earlier studies. Thus linear moving-average filters reproduce the observed AL with a correlation of 88% (AU: 75%) while linear autoregressive moving-average (ARMA) models based on the PC index produce in-sample single-step predictions with 98% and 97% correlations with AL and AU respectively. For long-term, out-of-sample prediction, the linear ARMA prediction from the PC index has an asymptotic prediction error which is at least 25% more accurate than the prediction from solar wind input. Nonlinear models are slightly more accurate than their linear counterparts, indicating a weak nonlinearity in the relation between the polar cap and auroral zone indices. The prediction-observation correlations are sufficiently high that models based on the PC index can be used for specification of the auroral geomagnetic activity. ¿ American Geophysical Union 1996