Predicting QSO Continua in the Lyα Forest

We present a method to make predictions with sets of correlated data values,in this case QSO flux spectra. We predict the continuum in the Lyman-Alphaforest of a QSO, from 1020 -- 1216 A, using the spectrum of that QSO from 1216-- 1600 A . We find correlations between the unabsorbed flux in these twowavelengths regions in the HST spectra of 50 QSOs. We use principal componentanalysis (PCA) to summarize the variety of these spectra and we relate theweights of the principal components for 1020 -- 1600 A to the weights for 1216-- 1600 A, and we apply this relation to make predictions. We test the methodon the HST spectra, and we find an average absolute flux error of 9%, with arange 3 -- 30%, where individual predictions are systematically too low or toohigh. We mention several ways in which the predictions might be improved.Comment: 17 pages, 4 figures, submitted to Ap